OK, I've played about 8 hours now. Still only in the atomic age of my first game! Things aren't moving too fast. But I'm having fun.
I'm playing as Spain on Emperor difficulty.
What I like:
1. The Policy Cards
These are a home run. They combine the best of Civ V's social policies--a huge breadth of options--with the flexibility and strategic richness of Civ IV's civics. Really great. I'm glad Firaxis didn't go with milquetoast bonuses--these things make a huge difference. Doubled adjacency bonuses or +100% military unit production is no joke. These are game-changers and it's really critical which ones you pick. I know I'm going to spend a lot of time thinking about how to best use them.
2. The District System
Another huge success. Placing districts is really fun, pillaging districts adds a great new dimension to war. Cities are far more specialized, unique, and interesting than they were in Civ V.
3. More Paths For A Civ To Develop
For the first time ever in Civ, I don't feel like I have to go all-out for science to be successful. Culture (and even Faith to some extent) are completely viable alternatives. This is great.
4. The Basis Of A Better Diplomacy System
I wouldn't call the diplomacy a triumph, because there are a lot of adjustments to be made and kinks to be worked out. The warmonger penalties, in particular, are out of control. But I like the idea of Casus Belli (even if the implementation leaves much to be desired), and I like that you can actually see the modifiers. Hidden agendas aren't nearly as bad as I feared, because they are actually not hidden--if the AI is upset because of the hidden agenda, they'll tell you why. There's the framework for a really rich diplomatic system here.
5. The AI Can Move And Shoot
I saw it myself! Incredible.
6. Wide Play Is Back
I just love this. Once again I can make the sprawling, multi-continent empires that are (in my view) the whole point of Civ. No longer does the game needlessly punish me. When my Scout discovered a rich and unpopulated island in the Renaissance Era, I didn't stare at the land wistfully and wish there wasn't a science penalty (as I would have in Civ 5). I bought a Settler and a Builder and sent them over! Awesome.
What I don't like:
1. The Warmonger Penalties Are Absurd
I conquered a couple Japanese cities in the Medieval Era. Little did I know that this would completely shut down diplomacy for the rest of the game. I got immediately denounced by every other Civ--even though I declared a Formal War--and they are still denouncing me, four eras later. Agendas and trade and the like don't even matter anymore. That one war was enough to earn me every AI's permanent hatred. That's not fun. Cut the warmonger penalty to something like one-quarter of what it currently is, or better yet, get rid of it altogether.
2. Eurekas Are Overpowered
I think 50% is way too much. They just completely dictate tech choices. Researching an unboosted tech is so terribly inefficient that I feel like I'm constantly being railroaded. 25% would be more reasonable, and would offer a more interesting trade-off between maximizing your resources and getting the specific techs you want the most.
3. Production Is Too Slow, Techs Are Too Fast
I think building districts and wonders takes just a little bit too long. On the other hand, I feel like I'm zipping through the tech and civic trees. To some extent this is mitigated by the relative dearth of unit upgrades (so your units usually don't go obsolete really quickly, like they did in Civ V), but still, this feels like it just hasn't been balanced quite right.
4. Ranged Units Are Overpowered
While Civ VI made some noble attempts to nerf ranged units (no more +1 range promotions, they don't exert ZOC), the fact is that archers are still devastating in human hands. Groups of them will effortlessly pick off any contemporary AI army. This kind of undermines the point of the Encampment district and strategic resources generally--why bother with that stuff when resourceless and cheap archers are so devastating?
Ranged units were way too good in Civ V, and they're still way too good in Civ VI. I'd like a nerf here.
5. The AI Doesn't Expand Enough, And Doesn't Protect Its Settlers
Now that wide play is viable again, I want that dramatic, headlong race for land that Civ IV used to have. But the AI seems content to stay put with 3-5 cities well into the Renaissance. To make matters worse, when the AI does send out Settlers, half the time it doesn't escort them. Combine that with the fact that captured Settlers stay Settlers (a bad design choice, imo), and you've got total brokenness. The AI should be hardcoded to always protect its Settlers. There's an escort feature now! The AI should use it.
6. The Game Is Too Easy
I don't think I've played very well. I screwed up in quite a few of my district placements, worked too many unimproved tiles for far too long, and have taken basically zero advantage of any of Spain's uniques (I'm not going for a religious victory). Despite that, I am easily doubling the score of any AI. I'm first by a wide margin in both Culture and Science. I feel like an Emperor AI should put up a better fight. I'm having fun designing cities and building wonders, but I want some challenge, too, and I haven't really gotten that.
Things I haven't made up my mind about include the housing/amenities system and religious combat. My initial reaction is that I like the former and dislike the latter, but I'll need a few more games to know for sure.
Overall, you'll notice that I heartily approve of most of the major design decisions (like the district and policy card systems). Most of my complaints could be fixed by just adjusting a few values here and there (except perhaps for my concerns about the game's difficulty). So I'm very optimistic about Civ VI. It's already a good game, and it's got the potential to be a great one.