(I should mention that I've had only Civ 6 for a month and I am not a pro by any means.)
In general I like what they've done with the design of individual mechanics to make them fun and interesting. For example with city building - in previous games you stack up all your buildings on the city centre tile and their benefits stack up there. In Civ 6, your buildings sprawl over the hexes within your city borders. You build industrial/culture/science/military/harbour districts, each on a hex near your city, and build your campus/barracks/market/temple inside those districts. There are all sorts of adjacency bonuses... some districts get boosts from adjacent mountains, industrial get a boost from resources with mines or quarries, some districts get a boost from being in a triangle with 2 other districts and so on. When you arrange things well, the tile and building yields go up and it's pretty satisfying. Wonders are built into specific tiles as well, and they also all play into the adjacency bonuses in various ways. It's a whole layer of new thinking on top of just stacking up buildings, and it's a puzzle to solve to get the most out of your cities that affects how you appraise city locations. I haven't cracked it yet but I really enjoy this part.
I really didn't like City States in 5. Civ has a wonderful system for building on resources, teching up and investing in military units... why on earth would you make an additional system where cities can't engage in regular diplomacy, where they monitor what tech level the world is at and spawn units on a timer? It was feature bloat to me; a new set of mechanics that replicated existing mechanics in a more basic and less organic way, and I never liked it. In Civ 6, that isn't completely solved (city states expand their borders but don't colonise) but they are better at letting the main civs put pressure on each other indirectly. You get a slow income of envoys and you spend them on City states. You can complete objectives for city states to get free envoys. You get bonuses for investing in city states and a special bonus for having more envoys with a city state than anyone else, including the ability to levy troops when needed. So if you have frosty relations with someone, you can attack and pay off a nearby city state to instantly get 5-10 more units to attack with. You are competing with all players for all city states so it throws up interesting situations and hotspots quite often. Again they refined a feature into something more fun than before.
The combat is pretty similar to 5, it's the same 1 unit per time system, except now you can merge units which helps avoid overcrowding. I'd say stacks of death were probably the feature I liked least in 4 and I think this makes fighting more fun.
Across the board there are improvements like that that I find myself liking the design of. AI leaders get agendas that change from game to game, that you can comply with or defy which affects diplomacy. Diplomacy and spying gets you an information access level with other civs, and you get gossip messages about what those players can see, to keep tabs on who is building a wonder, declaring war and so on. Your great people and archaeologists get great works and relics, which you install in your culture buildings for culture and tourism, with bonuses for collecting matching sets. You get the idea.
As someone who is not as fast to pick things up as they used to be, I have found that there is lots to do in this game but it's pretty easy to understand, at least to get playing. Maximising is another matter and I am not there yet. The interface and general presentation really help, 6 is extremely polished in that regard and very good looking. I guess in terms of advice I would just say to watch a Quill18 Civ 6 stream since he knows what he's doing and plays at a good pace.