
Stop The ADVENT Retaliation
Basically a refinement of the prior game's Terror missions, including there being a cluster of enemy types readily encountered in Retaliation missions while being much more unusual outside them. Most of the differences in details are basically straightforward improvements of the 'this is how Terror missions would've operated in the first place in an ideal world'.
So first of all, the objective is to rescue at least 6 Civilians, with a total of 16 Civilians on the map to potentially rescue, placed fairly randomly with a tendency to not be placed on high ground. (Though high ground Civilians are more common than in the prior game) Like in the prior game, you save Civilians by having a soldier stand near them, and alternatively the mission ends if no enemies are alive, and any surviving Civilians are considered rescued in that case. Also like the prior game, rescued Civilians start to run off to safety and just vanish partway through their movement -this vanishing actually bothers me less than in the prior game, since XCOM 2 actually defaults to the Skyranger simply not existing on the map at all. (Lost Towers is the only time it's visibly landed on the map) Where would they even go?
Unlike the prior game, Civilians automatically use Cover they're standing adjacent to, erratically giving them a non-trivial chance to avoid being hit. Indeed, if enemies move near them (Or if a Civilian is killed nearby them), they will automatically and for free flee to a new position, attempting to end next to Cover. (Though they don't actually try to make sure the Cover is useful, unfortunately)
This is all particularly important because of the overhaul to 'off-screen' kills; instead of the game rolling dice to arbitrarily kill people (And then, if inactive Chryssalids are present, roll more dice on kills to see if the Civilian becomes a Zombie), the game will select one inactive pod that can currently attack a Civilian under normal attack rules (Exception: melee pod leaders don't require line of sight to their victim), have their pod leader attack once, and reveal this happening in the fog of war.
This is a huge improvement; no longer are you arbitrarily incentivized to keep line of sight on Civilians as a nonsensical form of protection (Because EU/EW only selected Civilians you couldn't see in an attempt to maintain the illusion that actual enemies were performing the kills, rather than the reality that they're spontaneously keeling over for no reason), no longer does the game kill Civilians even when all inactive pods are nowhere near all out-of-sight Civilians... it also actually makes sense that you'd have some idea where weapons fire and death screams and whatnot were coming from, and depending on how distinctive the attacker's audio was it also makes sense to potentially be able to know what made the attack, so gaining sight on the attacker, though bizarre in a literal sense, is much saner functionality in outcome on that informational level.
It also has the benefit of being clearer communication on the actual rules for out-of-sight Civilian deaths, allowing a player experiencing the game blind to rapidly work out that only one inactive pod a turn can kill Civilians. That's a big improvement over EU/EW having really opaque mechanics for Terror missions, among other points letting XCOM 2 have clearer, tighter tuning on the design; the game can assume a player has at least a rough grasp of the rules because the rules are being pretty openly displayed to them. EU/EW hiding the rules meant it basically had to account for a lower bound of plausible competency, because players wouldn't necessarily know they were playing sub-optimally and wouldn't necessarily ever figure it out due to the opacity. (As opposed to playing sub-optimally by virtue of being unwilling to work on improving or something else that shouldn't be given accommodation; failure is what should happen if a player actively refuses to learn the game)
It's still imperfect; among other points, Sectopods break the 'one Civilian kill per turn' rule, and it's also an example of managing pod activation being much more important than I think the devs want (Certainly, more than I want), since active pod members can target Civilians without regard for the 1/turn rule inactive pods are held to... but seriously, it's a massive improvement, one of the things I was most immediately, unambiguously positive on when I was first playing the game.
Anyway, a particularly obvious change is of course the introduction of Faceless, where some portion of the Civilians you need to rescue are Faceless in disguise. I've been over this before in detail, but some points worth covering here; first of all, Faceless are not included in the surviving total Civilians at any point. If you're at 5 Civilians rescued and only 1 alive listed, that means there's an actual Civilian to rescue on the map, no matter how many Faceless are still in hiding, and you can thus actually succeed at the mission.
Second, Faceless counts in Retaliation missions are surprisingly un-random. Below Legend, there will be one Faceless on the map until you're late enough in the game, at which point there will be two Faceless, no random variation, while Legend starts at two Faceless and eventually adds a third. (I assume a specific Force Level threshold controls this, though I've never bothered to determine which one it is) As far as I'm aware this count never increases a second time, either. In the base game, this makes Faceless have particularly predictable corpse counts, since Retaliation missions have a not-quite rigid schedule, Faceless don't normally spawn in other missions (Except the final mission, but that's irrelevant to how many bodies you loot), and Retaliation missions always have you loot the bodies. War of the Chosen adding Savage and Beastmaster makes them a little more variable, but not much.
Third, it should be emphasized again that Faceless have a crucial nerf in War of the Chosen: in the base game, a Faceless that manually breaks its disguise can immediately act, whereas in War of the Chosen it will have to wait another turn, making it best to stop near Civilians but not try to rescue them if you're tied up in a fight already or your squad can't be counted on to immediately kill a Faceless. (Such as because the squad used up most of their turns winning a fight)
Fourth, it should be emphasized that in Stop The ADVENT Retaliation Faceless placement is basically just as random as Civilian placement. The game won't usually place two (Or three) Faceless close together, but that's not an actual rule the game holds itself to. (Or possibly it's supposed to be, but if so it doesn't actually work) So don't treat finding one Faceless in a group of Civilians as some kind of confirmation that the rest of the Civilians in the group are safe to approach; that's not actually guaranteed.
Also, something specific to Stop The ADVENT Retaliation that's somewhat Faceless-related is that the ability to rescue Civilians is actually a hidden ability found only on X-COM soldiers and SPARKs. That is, if you take control of enemies (Via Domination or Haywire Protocol), they can't rescue Civilians for your squad, nor can most units generated by your units (eg a Dominated Sectoid makes a Psi Zombie: the Psi Zombie also can't rescue Civilians), and if you mess with mods you'll find quite often that modded units also can't rescue Civilians! (Because the modder didn't remember to tell the game that eg SHIVs count) Conversely, disguised Faceless will still reveal themselves if such a unit passes nearby; you can still check for Faceless with these units.
Anyway, I noted earlier that Retaliation missions don't do squad Concealment, but the implications are different between the two variants. In the case of Stop The ADVENT Retaliation, it's one of the most important mission types in the game to try to bring your own Concealment into: you can't just advance cautiously, because Civilians are getting killed every turn most of the time and there's no guarantee the enemy will be close enough for a cautious advance to reach them in time. You can't just pick a direction and walk, because Stop The ADVENT Retaliation maps are generally very square, starting you in a corner, instead of the 'corridor' design a number of other missions use; it's easy to move someone to Cover and activate a pod who is now flanking that soldier, or even flanking multiple members of your squad if you moved several people before stumbling into the pod. A Concealed scout can let you quickly search for pods with minimal danger to the squad, and in fact can make it easy to outright ambush them with Overwatching soldiers standing just out of their sight; the sooner you start activating and killing pods, the better.
On a different note, a curious quirk of Stop The ADVENT Retaliation is that Alien Rulers are actually forbidden from attacking Civilians while inactive. (And have no interest in deliberately targeting them once active, for that matter) This is overall pretty useful, as it slows the rate at which Civilians get killed (Because if the Viper King's pod ends up the only one able to attack a Civilian in a given turn, no attack will happen, where it probably would've still happened if a regular pod had been generated and patrolled the same), and if you know about this quirk it can actually give you advance warning that an Alien Ruler is present. (eg if you deal with a couple pods, and then three turns pass with no further Civilian attacks... probably an Alien Ruler is the only pod remaining)
On the other hand, it does otherwise actively hide the Alien Ruler's presence, especially if you're not aware of the quirk to thus become suspicious when Civilians fail to die multiple turns in a row. So that can be pretty nasty for a learning player; indeed, Stop The ADVENT Retaliation is, in my opinion, the second-worst mission type to have an Alien Ruler spawn into, because you don't have squad Concealment, are pressured to hurry anyway, and the Alien Ruler can spawn basically anywhere on the map due to Stop The ADVENT Retaliation being weird about how it places the 'objective zone'. It makes it very easy to start the fight with an Alien Ruler off on the wrong foot, which can snowball into catastrophe, especially in the base game where Alien Rulers Ruler React basically anytime anyone does anything.
(The worst mission type is actually five mission types, but we'll get into that next post)
Overall, Stop The ADVENT Retaliation is one of my least favorite mission types. It's a fairly straightforward port of Terror missions, which I was already not very fond of, it adds narrative jank with unpleasant connotations (I really do hate how rescuing Civilians increases your Supply intake permanently; couldn't we have recruited these people into the Avenger instead?), and while the loss of Concealment makes thematic or narrative sense (ADVENT is already in a warzone, ready to shoot anything that moves and isn't clearly a friendly) it really hurts the gameplay in conjunction with how Stop The ADVENT Retaliation maps have a more chaotic, open design. It's absolutely possible to do stuff like pull two or sometimes even three pods on the first turn through no real fault of your own, in a way that's simply not possible on almost any other mission type, as almost all other mission types have better control over spacing and squad Concealment gives the player some ability to mitigate worst-case scenarios anyway. (eg you spot two pods while still Concealed, and then move the squad so only one pod is visible before engaging)
I much prefer...

Haven Assault
Haven Assaults at first glance appear to be a pretty mild variation on Stop The ADVENT Retaliation: you still need to rescue 6 Civilians for the mission to qualify as successful, there's still Faceless hidden among the Civilians, inactive pods get to attack while inactive, you don't start with squad Concealment, they're restricted to Shanty and can't have their biome be Xenoform...
... surprisingly, though, once you dig into the details they're radically different in execution.
So first, the overall framework is substantially different. In Stop The ADVENT Retaliation, Civilians are randomly peppered about, enemy pods are randomly peppered about, and enemies wander around pretty randomly. (That is, they 'hunt' for Civilians through fairly blind patrol routines; they don't actually know where Civilians are, not even if they've actually seen said Civilians) While the map will often generate to look like a reasonably coherent camp, placement of Civilians and enemy pods doesn't involve sensible rules you can intuit; Civilians don't deliberately hide in buildings or anything of the sort.
Haven Assaults instead organize the map into two distinct phases, each tied to a separate location, one not much more than a Dash from your starting position, while the other is several turns of Dashing away and specifically beyond that closer one. The closer of these is phase 1: a cluster of 4 Civilians, guarded by a pair of Militia, with two enemy pods descending upon them, while the further is phase 2, a cluster of 9 Civilians guarded by 4 Militia, with four enemy pods descending upon them either a couple turns after you cleared phase 1 or after too many turns have passed in general.
Oh yeah, the Militia; these are friendly soldiers with their own phase after the enemy phase, who contribute some weak gunfire to the defense. Militia have 6 HP, 85 base Aim, 12 Mobility, 50 Will. They technically have 5 Hack and access to Suppression, but they'll never get an opportunity to Hack and they'll never use Suppression. Their damage is 2/4/6 based on how far into the campaign you are, with crits adding 1/2/3 damage. Their rifle, curiously, only has 3 ammo, unlike your own Rifles. It also doesn't have Aim climb, so their impressively high base Aim -better than most of your Colonels!- is deceptive, as they'll actually still miss point-blank shots 15% of the time.
Their AI is kind of frustratingly terrible, unfortunately; they have the usual AI obsession with spending an action point on movement, even if it's not productive, including they rarely reload in place when out of ammo and so often effectively skip a turn. They're also not very good at picking relevant Cover, and are prone to not flanking enemies, probably in part because they refuse to move too far from their assigned area. They also share the usual AI propensity for abandoning high ground quickly, exacerbating their issues with accuracy. They'll still often contribute a fair amount of work, mind, but they're pretty bad -and it's really obvious they're bad, because the game permanently reveals their combat zone once their phase activates and always shows them shooting even if they're in a non-revealed location, so you'll unavoidably see their dubious decisions. Oops!
The Militia having their own phase, by the way, is because they're technically their own faction, much like Lost are. Unlike Lost, they're willing to spontaneously exchange fire with enemies in the shadows -in fact, one of the main bugs of Haven Assaults is that phase 2 Militia often open fire on phase 2 pods before phase 2 has properly started!- and notably this interacts with enemy pod activation the same way Lost do: if you have a Concealed soldier in the area able to see the pod being shot, the pod will activate in response! Whereas if your soldiers can't personally see the pod being shot, the pod won't activate in response to being shot. So, uh, don't run a Reaper ahead to watch Militia valiantly defending their charges; you will actually make things worse with your voyeuristic stalking.
Unlike Lost, Militia are friendlies, and don't have pod activation mechanics of their own. (Well, the phase 2 Militia sort of do, but my point is they are perfectly happy to move about and fire even if your squad hasn't spotted them yet) Indeed, not only are they friendly, they're actually counted by the game as Civilians for rescue purposes, bringing you to a total of 19 rescuable folks instead of 16.
Speaking of rescuing, this is also different: you do not rescue Civilians in a Haven Assault by standing next to them. Instead, the (surviving) phase 1 Civilians -but not the Militia- are automatically rescued all at once as soon as the two pods assigned to attack them have been wiped out. (Reminder: if a Codex clones itself, or a Chryssalid cocoons someone, these new enemies are not tracked for determining whether the phase 1 group is safe to run) The (surviving) Militia will instead run on ahead to the phase 2 group -by 'running' I mean 'running the full distance instantly, out of turn order', not 'manually spend their turns trying to run to phase 2'. It's... weird.
Anyway, as for the phase 2 Civilians -and all the Militia- you never perform a mid-mission rescue of them. You simply win once every enemy is dead, with all survivors treated as rescued, exactly as will happen if you kill every enemy in a Stop The ADVENT Retaliation mission. Notably, since you can only rescue 4 Civilians mid-mission, and still need 6 Civilians to avoid mission failure, this means you haven't removed the possibility of failing the mission until it's actually over. (Mind, you could always fail a Stop The ADVENT Retaliation by virtue of your squad wiping...) I very much approve of this change; saying the player has completed their objective of protecting civilians as soon as less than half are... wherever they run to... is honestly pretty weird, and opens up unpleasant questions in conjunction with the ability to Evac from most missions; a player might honestly think they can simply Evac as soon as six Civilians are rescued and get full credit for success that way, even though that's narratively somewhere from 'extremely gross' to 'flagrantly nonsensical' because the mechanics seem to imply it's an option...
... and by the way, they'd be unpleasantly surprised by discovering that actually Evaccing automatically fails any mission that doesn't actually require the squad Evac. Whoops!
So this change is nice for avoiding that mess.
Also, in Haven Assaults Civilians will never move (This doesn't include Militia, to be clear), unlike Stop The ADVENT Retaliation Civilians being willing to scramble for Cover. This makes them on average a little more reliable about dying, as the game doesn't make any effort to plant them adjacent to Cover; usually some of the phase 2 Civilians will be adjacent to Cover, and it will intermittently even be relevant Cover, but you shouldn't count on it and phase 1 Civilians in particular are basically always completely exposed.
Anyway, we're not done, though. Still lots of differences to cover!
So next is Faceless: in Haven Assaults, all Faceless always spawn among the phase 2 Civilians, never among the phase 1 Civilians. (Nor will they be disguised as a Militia) So feel free to wander near the phase 1 group. Faceless are also really pathetic in Haven Assaults, thanks to the fact that unlike Stop The ADVENT Retaliation it's not actually inherently desirable to approach Civilians. In conjunction with War of the Chosen removing their ability to act on the turn they reveal themselves, they're extremely unlikely to ever hurt your troops unless you're specifically meleeing into the phase 2 Civilian mob. In fact, a Faceless revealing itself in a Haven Assault often results in its death before your turn, as Militia are quick to shoot them and take their turn after the Faceless reveals itself but before your turn, and Faceless don't use Cover nor have innate Defense; Militia thus find them to be a very attractive target by virtue of reliably hitting them. (As Militia AI does, in fact, overall prioritize making accurate shots, same as most XCOM 2 AI)
Then there's the opposition more generally.
First of all, I should immediately point out that in Haven Assaults enemies are not held to the 'one inactive pod per turn' rule for attacking Civilians and Militia. Every inactive pod can attack every turn. Furthermore, Haven Assaults have special pod counts completely divorced from Force Level and difficulty: they simply generate 6 pods, no matter how early or far in the game you are and without regard to whether you're on Legend or below it.
"Wait," I hear some of you mumbling in horror as you crunch the numbers and realize they give mission failure on turn 3. "How do you win, then?"
Well, first of all Militia can actually survive being hit, at least until you're later in a run. (And unlike Civilians they don't effectively have negative 20 Defense, and in fact are semi-reliable about pursuing Cover, so they get hit less consistently too) More importantly though, as I implied earlier enemy pods are tied up in the phase mechanic: initially, you're in phase 1, and only the two pods assigned to phase 1 are allowed to carry out their task of charging their phase's Civilians and attacking them. The four pods assigned to phase 2 have to wait until phase 2 starts -and unlike the phase 2 Militia, phase 2 pods do not buggily make attacks earlier than intended. Indeed, even once phase 2 starts, the pods assigned to it take a turn or two before they properly wake up and attack.
Furthermore, the pods of both phases usually start a decent distance from their targets; it's not unusual for them to spend a turn on advancing even once they 'wake up', needing another turn to get in range for actually attacking. Dedicated melee pod leaders often need two turns of advancement.
It's also worth pointing out here that ranged pod leaders cannot attack a Civilian the turn they stumble into your squad and activate. This is actually true of both Retaliation missions, but it's a lot more useful in Haven Assaults, as the pods have a clearly-defined location they actually try to advance on -and phase 2 of Haven Assaults usually has most of its Civilians hidden inside a building, vehicle, shipping container, or other object that substantially blocks line of sight, forcing them to get closer so they can actually attack.
Unfortunately, melee pod leaders absolutely can charge into view, killing a Civilian, and activate now that you've seen them. This is one reason why Haven Assaults sometimes deciding Berserkers should lead every pod is so problematic; because it curtails your ability to actually throttle back Civilian death rates by forcing pods to activate in the form of stumbling into your squad on the enemy turn. They still can stumble into your squad and thus 'lose' an attack, but you can't actually force it.
Anyway, an extension of this unique pod generation behavior is that Chryssalid loner 'pods' that Burrow on the first turn can't occur in a Haven Assault -at least, not normally. (I've yet to have Infestation trigger and then see Burrow-pods in a Haven Assault, but am unsure if it's impossible or I just haven't had it happen yet) This makes Burrowing noticeably rarer in War of the Chosen -it's not unusual for a War of the Chosen run to only see Burrow-pods in the Psi Gate mission, since Chryssalids are so prone to spawning in only one Retaliation mission, and all the new ways for Chryssalids to show up in War of the Chosen are not Burrow-pods. (Though of course they can still elect to Burrow if they lose sight of your squad) I'm unsure if this is an intentional reduction to Burrow's relevance or a happy accident, but I appreciate it regardless, given Burrow's mechanics are janky in such an unpleasant way; even if Burrow's bugginess was resolved, it would still have design issues. (Like that it's basically melee Overwatch, only it ignores anti-Overwatch tools and lacks Overwatch penalties) Reducing its presence helps some.
Another consideration is to do with Chosen and Alien Rulers: in both cases, they always spawn over by the phase 2 zone, never the phase 1 zone. The Chosen completely ignore all this phase stuff, though; they will teleport in on the first enemy turn and immediately do their usual thing. They do not wait for phase 2 to properly start. (I'm actually unsure how Alien Rulers behave on Haven Assaults; I've had them spawn into them far too rarely, and mostly early on before I had a handle on the mission division)