Civ3 was pretty good compared to Civ2. I think it wasn't all that drastic of a difference, more like additions made. Units started getting bonuses vs specific units iirc, like spears double vs horses, it's been so long since I played I don't remember if that came with 3 or 4! And then adding health to units was a big change but it begain with civ2 and hit points. Civ3 just made it more sophisticated. And then they added resources which was a big change and a move in the right direction.
Other than that corruption and tax slider system was largely the same just expanded on. Settling was mostly the same, wonders too. I can't remember exactly but I think caravans worked in both too. Obviously diplomacy was a lot more enhanced especially since you could trade resources.
Then 4 came and while it expanded on a few things, it was just a leap forward. Some stuff, a lot of stuff, was redesigned. Like corruption and waste, those things were very annoying in civ3 and 4 replaced them with city maintenance. I liked it a lot better. Also gone was building maintenance. Good idea imo, you don't feel bad building stuff now, it's more fun, even if it's not worth the opportunity costs. And then civics added a huge new flavor to the game.
And just the tech tree in general and how units work. The rock paper scissors concept meant many strategies would work. You could go cavalry rush or try to get cannons, not usually both. If enemies managed to get infantry but not railroad maybe you quickly try to get oil and bombers. Lots of options.
Where I feel civ5 failed was obviously 1upt sucks, makes the game CRAWL late (and is really why I mostly hate it. finishing games is a chore.), but mainly the philosophy. Everything builds linearly. Like religion is just another +1 system. You pick a perk and it gives you +1 global happiness per city or whatever. Civic policies same deal, accumulate culture and buy policies or whatever they are called and it gives you bonuses. Nothing is a trade or a slider. I hate population producing research, it ties everything to empire size almost directly, which then becomes limited by this global happiness, it's so darn annoying. You can't run deficit research and make it up selling techs, you can't do anything complex and cool.
Anyway weekend is coming soon, I'll try to post vote results Sunday night or Monday.