Following something like a 40 hour Normal campaign, here are my mature reflections on XCOM 2 (though some of this may change with difficulty).
Interface
Generally the interface is a slight improvement over - though very similar to - XCOM, though unit placement on tactical maps seems a little too sensitive and misclicks are easy. The big gripe is the two-step process to get back to the Geoscape from any given Avenger screen, as you have to go to the main base screen to get the Geoscape icon back.
Strategy
The big one given its limitations in XCOM. There's a definite nostalgic feel to being able to move from site to site around the map, and the decisions presented are meaningful. There are usually enough varied targets to choose between at any given point (and if there are none available, there are always resistance cells to contact or radios to build) that you rarely get the XCOM feel of sticking the game on fast forward until the next mission shows up. There's some imbalance between options (scientists are less important than in XCOM past the first 2, Engineers moreso; intel is much more valuable than supplies once the black market opens) and consequently some redundant choices you're rarely if ever going to pick (you're never going to switch HQ away from gathering intel, and you're never going to buy scientists unless you fail the first month's VIP mission). Given that these have always been the bread-and-butter of X-COM, it's a shame that the setting doesn't allow for aerial combat or for downing UFOs (and so no UFO maps unless - and I've been told they can - show up as resistance leads), but it makes sense. Alien interrogations are also missing, which is a shame especially as there is now an intel resource that could be derived from them (instead there are data cache drops that can serve the same function, but without the backstory). Another change in the age-old formula is that, with resistance contacts providing fixed income that can only be reduced by failing terror missions, the monthly report is even less meaningful than in XCOM - what's more the Spokesman's choice of praise/disappointment seems to correlate badly with what you actually accomplished.
The Avenger is rather a disappointment, simply because it offers no real challenge - as long as you're always excavating to prepare for the next facility unlock, once you have your core foursome of Guerilla Tactics, Power Relay, Advanced Warfare and Resistance Comms, you only really need to build the newest facility you've researched and even when you complete the research tree there are more rooms than you need facilities, as they can all be upgraded. While a central position for your workshop may be of some use to give greater access for your workshop GREMLINs, you may well have enough engineers on staff by the time you want the workshop and/or excavate to a good spot that it doesn't much matter, and nothing else cares about where you place the facility (save in relation to a workshop). This is the only area in which the game is a step back from the last one.
Research is very basic; almost nothing past the earliest tech stages has a prerequisite tech, only resource requirements, and for the length of the game a little too fast once you have 4+ scientists. Shadow Chamber research should be a trade-off with actual research, rather than something that unlocks only when you have no other research left anyway. It's possible higher difficulties address this to some degree, as research is presumably longer there.
Engineering is much more interesting and the random outcomes of Proving Ground projects are an interesting and thematic touch. With so many buildable options there's inevitably a lot of redundancy, though. Again perhaps related to difficulty, but I found myself swimming in alloys and elerium crystals, so these resources were mostly meaningless as constraints on construction past the early game.
Maps
One of the suggested downsides to procedural maps is that, unlike XCOM's crafted maps, however different the scenery - and XCOM 2 scores well on this front, with welcome nods to the original game in its woodland, farmland, desert and snow maps (not sure I've seen a jungle map, but outside South America - which I didn't reach on my campaign - the only zone that seems likely to produce these is New Indonesia, and I only had a base mission there) - the maps all tend to be very similar in structure, and so lead to similar tactical games whatever the map. XCOM 2 definitely bears this out - most maps are a bit too open, without restricted corridors of attack to allow alien ambushes (I felt this particularly on the story missions, which offered less relative challenge than the corridor-based battleship missions of XCOM) or especially good opportunities to flank.
While the handcrafted approach did lead to a too-small number of repetitive maps, I wonder if some mix of procedural maps and a number of tailored maps that offer different types of challenge would be an improvement. Story missions and what passes for a base defence mission (which in the one case I had was basically shooting at aliens in a field, with the bonus of turrets and reinforcements - pretty sure base defence shouldn't be easier than a typical mission) feel rather anonymous, except for the black site (which does seem to have specific map components coded in) and the final mission, which is corridor-based - even the twist of having fewer soldiers than normal in the penultimate one doesn't make it feel different.
Tactical
Concealment is fun (and vigilance is annoying). I'm not altogether sure of the logic that suggests getting to free-kill the first pod you encounter should make the game more challenging, though. Losing concealment prematurely is dangerous, which is where the fun comes in, and I lost a few playthroughs early on before getting the hang of the system - but once you train yourself to be cautious early it's basically nothing but bonus. I think part of this comes down to those too-open maps - there aren't all that many situations where alien patrols can cut you off completely, forcing a reveal you don't want (though when it happens it's rewarding).
I like the patrol system to some degree, although it comes with narrative problems (Sectoids et al. openly patrolling with ADVENT peacekeepers seems off thematically, even moreso the later, more combat-capable aliens, and it makes no sense at all for Codices). At least on Normal, however, only the heavy MEC ever goes onto overwatch as a reveal reaction, and so as in XCOM without Second Wave you always get a free turn to kill any pods you don't accidentally trigger late in your turn. This was a sufficient (and justified) cause of grumbling in the first game that it's sad they didn't address it even as well as Second Wave did.
Somehow, despite all of this the tactical layer is more challenging than in the first game, and very enjoyably so. The emphasis on activated abilities, most of which have a cooldown, also leads to interesting decision-making in combat, as does the variety of upgrades available from engineering.
The tactical game also introduces some X-COM elements missing from XCOM - fire (which irritatingly seems able to randomly start on your soldiers in some cases, I think as a result of Grenadier weapons overheating), picking up bodies, and loot being the main one. Disappointingly loot is handled with the same disregard for game context as in hack 'n' slash RPGs, bearing no relation to the gear the dead unit was actually carrying and often being thematically implausble (carrying unattached weapon modules around, for instance, that ADVENT and aliens can't actually equip. Modules would be more satisfactory as random proving ground projects resulting from a generic resource like elerium cores).
Mission variety is a little limited - most missions are timed either because there's an actual timer, or because the objective is 'rescue 6 civilians' or 'save a unit with X hp' where the AI is programmed to kill X civilians a turn or deal X damage a turn unless the attacking pod is interrupted. This results in less dynamism in retaliation missions in particular than is welcome, and may also contribute to poor AI performance for Chryssalids, which don't have their XCOM/X-COM habit of massacring civilians and turning them into zombies.
Game progression
Tactical progression generally seems better in the broadest sense than in XCOM (or X-COM), with difficulty actually becoming greater towards the late game after a mid-game lull into complacency. Chryssalids have already been mentioned as a glaring exception - they're conceivably okay on terror missions, but they actually turn up in base missions like the final one where they not only have nothing to eat, they don't have surfaces they can burrow into (a nice and underexploited new alien ability that really should show up much earlier in the campaign). There are other exceptions as well - Berserkers are weak, and it was an odd decision to bring them back while more interesting aliens like Floaters (yes, they evolved into Archons, but those are too late-game and too weak themselves) and Seekers were eschewed. The Archon is, indeed, a Floater, but without the fly high ability that made Floaters dangerous and being too late in the game for its impact - it's good at dodging, but not so good at actually damaging. The Gatekeeper (aka the Cyberball) would be very dangerous if toned down slightly and introduced at the same stage as its Cyberdisc precursor, but mostly all it does is animate psi-zombies en masse, which aren't good individually even in the early game and aren't good en masse this late.
At the same time, early aliens become redundant too soon - Sectoids are nullified by mindshields and killed outright by gauss weapons. Vipers appear perhaps a little too late to be truly dangerous, as they're a threat when they first appear but cease to be one very quickly. Unlike the last game, there are no 'Heavy' versions of non-ADVENT aliens, and there seems little reason for this absence. The gap between the decline and eventual near-disappearance of Sectoids and the first appearance of Gatekeepers (which have only a limited suite of psi-abilities that I've seen) also leads to a very long gap when the aliens don't field psi units at all. And mind control is only threatening on Avatars, since they get to teleport out of sight after doing it and are hard to kill anyway.
Narrative
The narrative generally hangs together, though setting it 20 years later than the first game with nothing much happening in the interim is an unnecessarily and implausibly long gap (apparently in all that time Bradford's group hasn't killed a single ADVENT, since it's only in the tutorial mission that he learns they aren't human). Similarly the aliens seem to have been sitting on their hands all that time, starting the Avatar project only when we come on the scene ... despite the fact that it's revealed to be their ultimate objective in staying on Earth to begin with. It's better-told than in the last game and, while it ends in the same place, it does lead to a sense of intrigue and discovery better befitting 'Enemy Unknown' than the game that bore that tagline ("what are the aliens doing? Why are they here? Let's research something else and hope they tell us in the final mission"). I like the new characters - particularly Shen - and the relationship between Shen and Tygan is better-described than that between Shen's father and Vahlen. Also, there are more story cinematics although the story is less intrusive on the overall gameplay (there are only five story missions and two 'capture the alien' objectives in a longer and more open strategic game). Indeed it probably should be better-integrated into the campaign - the narrative research tree is entirely independent of the stuff you need for gameplay, so where in X-COM you'd more or less incidentally obtain story leads as you played and in XCOM you needed to reach a certain story point to unlock psionics, in XCOM 2 you can if you like ignore the story until the end (the Avatar clock is a bit pointless, since it takes forever to fill and even when it does it's not irreversible) - although obviously the earlier you tackle it the lower-level the aliens will be, and I'd rather face a Blacksite where the toughest enemy is a MEC than one with Sectopods and Andromdons.
Speaking of Andomedons alien names are well-incorporated into the lore except, of course, for the ones you want explained. Andromedons aren't explained and there's no indication they're thought to be from Andromeda, and Gatekeeper is fourth-wall-breaking as the name is applied to the loveable ball before you ever learn they protect the psi-gate.
Overall
Nostalgia aside, XCOM 2 is probably the best XCOM game so far (including the original trilogy) but certainly still has irritations and a few of the original game's elements - such as loot drops reflecting the actual gear aliens carry, and missions in downed or landed UFOs - are missing. Top priority for DLC and patches, I'd suggest, would be adding a variety of set maps for things like alien facility missions, in much the same way the original UFO had procedurally generated maps for most things but fixed maps for the alien bases and UFO designs.