As someone who played Civ I back in the day I will say that Civ 3 was my least favorite (havnt played 5 so I have no comment on that).
Civ 1 was a great new style of game for me when it came out, who dosnt want to build up a civilization and conquer the world.
Civ 2 was just Civ 1 with more... more units, wonders, and tech, but the biggest difference between the 2 was the combat system. I remember never building battleships in Civ 1 because they had this really bad habit of dying when attacking a phalanx. Once I remember the AI trying to take one of my cities, he took out all of my defending mech inf's, but then on his last attack of the turn my settler took out his last attacking unit. Civ 2 fixed that in battles where one unit should clearly win it always did.
Civ 3 I was very excited about when I was first reading about it, resources that affected what units you could build, generals that could make armies and the my favorite new idea, cultural borders seemed a great idea. I have always built fewer cities spread far apart because I never build cities with less than 3 special resources (well unless I needed a canal or could close off a choke point). The problem with that of course is that any AI you make friends with comes and builds cities in your territory because there is space between your cities, I figured cultural borders would let me actually try to play nice with other civs for a change and give diplomacy a try. Well not only did the cultural borders not stop friendly AI's from building cities in my territory but the combat system was "refined" to function much more like the civ 1 system again. Every half dozen to a dozen attacks the game decided that a unit of mine should die, no matter what it was attacking. I never played more than a few games before I gave up and just went back to civ 2.
Civ 4 I gave a try when it came out and was rather happy with. Cultural borders let me build spaced out cities without AI's settling in between. Combat although not perfect works again (Im not a big fan of early game combat in civ4 with all the counters between the units so that you need huge amounts of units to capture anything since the defender always seems to have at least one unit to counters all your attacking strengths so your always loosing a few units with every city you take, there is a few other things I missed from the earlier games as far as combat goes as well, but with modding you can always change what you want to your hearts content). Religion did take some adjusting too, but I enjoy it.
Civ 4 is what I play now, i havnt tried 5 yet (although it really sounds like 1upt has some issues to work out still before I would enjoy it). Civ 2 I sometimes get the urge to load up, but whenever I get the urge it goes away before I can get it installed since it takes mucking around with to try and get it to work on windows 7.
So while this is mostly just me rambling on about a game I have spent way to much time playing over the years, if you find that what annoys me about civ 3 also bothers you then I would say that Civ 4 would well worth giving a try. If those things dont bother you then I would be more inclined to try a different game instead and give 4 or 5 a try when you feel the urge to play Civ again in the future.