IMO IV>VI>V>3.
I really don't understand how anyone could like 3 the best. I started with 3 and played it for years when I was in like middle school and I had a ton of fun with it. But IV is just an improvement in pretty much every way. The graphics are just unacceptably bad, the map is freakin 2D.
@agonistes I appreciate what you're saying, I just completely disagree...yes, Civ 3 results in the most populated giant earth maps because of its affinity for completely uncontrolled ICS but that isn't actually a fun game at all. There just isn't really anything in Civ 3 that IV doesn't do better.
I pretty much assume anyone who prefers V started out with it as their first civ game. It's just not that great, IMO, when it first came out it was a step down from Civ IV, even with the expansions in place it had improved graphics and changed some features but just wasn't as fun gameplay wise. And now just a few months into Civ VI release it's already a much more fun game. Like, going from 3 to IV they mostly just refined and added features, IV to V was a pretty big overhaul with a lot of major changes but V to VI is once again mostly refining and adding features. There's just nothing about V that really stands out to me, VI is better and I wouldn't go back for nostalgia. Oh, and the penalties to expansion are just the absolute worst, there should not be areas of the map that no one has claimed in the modern era, it's just stupid.
Now as far as IV vs VI. Both are excellent games, no doubt. But IMO the difference is just in the feel they have, the general scope of the game.
Civ IV feels epic. You aren't really your civ's leader, you're some godlike guiding force pulling the strings. It really feels like you're building a civilization, not worrying about the mundane details but strategically planning and expanding on a grand scale. When you fight wars, you're sending vast armies with huge numbers of troops to their death. It's IMO the most suitable for the scale of a civ game where you're literally going from 4000BC to 2050 AD and developing the entire world.
Civ VI just feels a lot less epic. The player's perspective seems more limited, like you're the leader of your civ just doing what you're able to to lead your people. You don't just plan where your cities will go and where your people will settle, you have to worry about how the cities themselves develop, what grows where, you have to manage trade routes individually. Combat isn't an epic massive scale bloodbath, it's yet another tactical minigame. That's really my issue with Civ VI (and was true for V as well) - it just feels more gamey. You're accumulating victory points. You're focused on doing what you need to win. Civ IV feels like a grand strategy game, it's got quite a sandboxy feel to it, like you're painting the world. VI is about winning the video game - on high difficulties the AI will win by like turn 350 if you don't win before that and on lower difficulties there is just no challenge at all. Moreover it's not a pure grand strategy game like IV - it's like a city-building game, and a tactical combat game, placed into a grand strategy framework.
The franchise really went from grand strategy feel, to an artificial tactical minigame, with 1UPT in Civ V. Like by any reasonable measure that represents the size of a planet on a map, each tile represents a land area of hundreds of square miles. So when you have an archer attack a unit 2 tiles away, your archers are shooting their arrows hundreds of miles to hit the enemy... There's just no way to integrate this kind of thing in the grand strategy framework, it's sacrificing any semblance of realism for 'fun' tactical gameplay.
All that being said, I love Civ VI, it's really well done, it's a great game and it's a ton of fun. I have a PC and a Nintendo 64 and Civ is all I play on the PC, and I've been playing a ton of VI. All those sacrifices for gameplay result in a really fun game, and most of the issues from V are smoothed out. And there are some features like religion that really are represented more realistically and organically than in IV. Plus you can't argue with the graphics, IV is still playable but...barely lol. And it's fun keeping up with the DLC and game updates. Civ VI is an awesome game and is going to be even more awesome with expansions, it does what it does very well it's just a different feel from the old civ games.
Also, Civ IV FfH is hands down the best fantasy strategy game of all time