I like Civ6 a lot. It's a different game, so cannot be compared to Civ3, but each has its own benefits.
In Civ6 I like the fact that all nations are very varied with lot's of different traits and capabilities and therefore different strategies that can be implemented with different civs. (However, it also means that multiplayer is much more imbalanced than in Civ3, unless you give everybody the same civ...)
Also the combat model is much better than the kind of "crude" combat model in Civ3, and the promotion tree for units is very nice.
In Civ5 I didn't like the stupid happiness model, which leads to bizarre behavior, like if you are successful in a war and keep capturing enemy cities, your population keeps getting unhappier and unhappier up to the point of revolt, while when you are getting beaten badly and getting your ass handed to you, your population becomes happier and happier... Yeah, like in real life... very authentic...
Civ4 was for me the worst of the entire series so far. Got it in 2005 from my brother-in-law, tried 2 games and then uninstalled it in disgust. It did not feel like "Civilization" at all, did not ignite the "civ fever" for me, and had lots of stupid concepts I didn't like. The combat model was too complex, with a maze of units, counter-units and counter-counter-units. They way, artillery type units worked, was simply braindead (every cannon immediately blowing up and getting destroyed upon firing the first shot, yeah, very realistic... that was a major step backwards from the artillery units we had in Civ3...), and the promotion tree was not a "tree", but more a "jungle" in which to get lost...Too many steps in the wrong direction. (And I didn't even mention the ridiculous kindergarten graphics and look&feel yet...)
So for me, Civ4 feels like a screwed-up version of Civ3 (sorry, patinthedesert...

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Civ5 was a step in the right direction again, I liked it from the beginning despite its shortcomings like the bad happiness model. It already had many of the features that later got continued and improved in Civ6, like the combat model, the clear-cut promotion tree, the one-unit-per-tile rule which requires strategic thinking and well-planned logistics in warfare, a good religion model, diverse nations for trying different strategies, lot's of fun stuff.