I spent thousands of hours on 1-3 and loved them all. Civ4 and Civ6 are the only versions of the game that I still play. I still love Civ4 and continue to play a lot. However, this being the forum it is, I am going to defend Civ6.
I hated Civ5 and gave it up after a month or so. Civ5 introduced a s***load of new concepts. Some of them were interesting, like 1UPT, city states and policy cards, but poorly implemented. Some of them, like puppet states and road maintenance, were just stupid. What fun is there is having a city which the AI controls? Or getting punished for making essential ways for moving units from one city to another? Then there's the diplomacy model. For some reason, the developers thought it a good idea to create a AI which was insane and impossible to negotiate with. How stupid is that?
Some of the innovations, like global happiness, simply failed to achieve their objective. This was supposed to make it increasingly difficult for players build new cities. Every version of Civ has a mechanism for this purpose In Civ1-3, it was corruption. In Civ4 it was city maintenance. Players proved that it was easy to get around global happiness so for two years, the developers tried to find ways to fix it. In the end, their solution was to punish building new cities so brutally that the player was forced to sit on four or five cities. The result was an empty map with each civ in a little corner never growing towards each other. This is simply not a game of Civilization at all.
Civ6 dumped the bad concepts from the previous version. The others it improved. The diplomacy model is admittedly not as good as Civ4 but at least it is again possible to work with the AI. It improved on concepts that it kept. In Civ5, players were forced to select a tree of policy cards very early in the game and never change it. Now it is possible to change the cards used every few turns. The worst aspects of 1UPT were mitigated by allowing settlers and workers to be in the same tile with military units and by making it possible combine units together to make them more powerful.
Most importantly, the developers found the best method yet to make new cities difficult to build (Civ4 is a close second here). And it is simplicity incarnate. All they did was to make each settler more expensive to build than the previous one. As there should be, there is an increasing cost to each new city but it is again possible grow your empire. The map fills up. Civilization is back!
There are great new additions too. Districts make for a trade-off between making city improvements and tile improvements. The best strategy games provide interesting choices for the player. Builders, IMO, are superior to workers because there is so much less micromanagement. Religion actually has a purpose of its own unlike Civ4 where it was simply a part of the diplomacy system. Each of the win conditions requires a completely approach to growing your civ. In Civ4, a cultural victory indeed requires a different approach but the others are all pretty much the same with a slight divergence at the end.
I am going to defend 1UPT too. Optimally moving and placing your unit is an interesting and quite difficult tactical problem. There is a serious cost to every unit you lose. OTOH, sometimes it's worth it. What interest is there in building a huge stack of units and ramming it up your opponent's butt? War in Civ4 is really an economic problem, not tactical. High difficulty Civ4 wars are mostly about slaving out an army of elepults or cuirassiers. Now it is true that an AI able to deal with the simple task of butt-ramming but that is not a point in its favour. If we wanted a perfect AI, we should play tic-tac-toe, not Civ.
Oh yes, the AI. Contrary to the received opinion on this forum, the Civ6 AI is much better than Civ4. It is sufficiently capable when warring. More importantly, it is decently competent at everything. Civ6 is an extremely complicated game - perhaps too complicated - but the AI is reasonably capable of handling all aspects of it. In contrast there are things in Civ4 that the AI has absolutely no clue about. Espionage and Diplomatic votes come to mind.
The Civ6 AI also understands how to achieve each of the victory conditions. In Civ4 the AI did actually plan to achieve culture. Often, though, it would do so when only a few turns from some other win and thereby actually lose the game. This is because it has no understanding of any the others. It simply builds stuff and wages wars until finally it stumbles into a win. Usually space but sometimes domination. As for a diplomacy win, well forget that.
Things I don't like about Civ6 are mostly design choices or oversights by the programmers, not errors in the fundamental design. They have a penchant for monochrome colour schemes which make it nearly impossible for my old eyes to see through. For example take the part of the map you have revealed but cannot currently see. It is displayed in shades of brown. Why can't there be a toggle which lets you see things clearly? For example, to choose where to place cities. There also is a serious lack of numbers to help the user make decisions. Combat odds are displayed as "Major Victory" or "Minor Defeat" instead of the precise values you get in Civ4.
And roads, dammit! There needs to be a way to make roads. The movement rules exacerbate this problem. For some reason, Ed Beach seems to like forcing the player to trundle units around the map one tile at a time. What's more you can't just point a unit at a destination and let it go. A couple of turns later the pathing algorithm will discover that another unit is blocking it four tiles away and send it on some insane alternate path to get there. In practice every unit has to be moved individually on every turn. Ugh.
Finally I would like to mention what I consider superior about Civ4. First all, there is the User Interface. BUG is clean and simple with most things on the main screen and everything else just a mouse click away. Civ6 is decent here (far better than the abominable Civ5) but Civ4 is simply excellent.
Both IV and VI offer frequent and interesting choices for the player to make. This is in stark contrast to Civ3 where there was only one good government or Civ5 where the player is far too often confronted with an choice between two bad alternatives. However IV strikes a much better balance between depth and complexity. VI is simply too complex. There are too many sub-systems and too many things to learn. Things like District adjacency rules come to mind. Every district has its own rules and they interact with those of other districts. Much much for my old brain to remember.
All in all I like both games a lot and continue to play them both. Civ4 is ten years old and it has aged very very well. The new kid on the block is a worthy contender for the crown.