There's a few reasons I prefer Civ3 to Civ4, but the biggest one comes down to the lack of epic scale in most Civ4 games. Even on a standard-size Civ3 map the empires are a decent size, whereas on even large Civ4 maps the empires feel tiny. Scale up the map and Civ3 can feel really epic, whereas it's quite rare to get that feeling in Civ4.
Other reasons include:
*Some ground combat elements, such as artillery being throwaway units rather than bombard-at-range units (against other units), and the existence of bonuses against certain types of units resulting in a game that generally skews more towards defence, unless large amounts of artillery are sacrificed to each conquered city.
*Air combat elements, such as not being able to destroy buildings with aircraft.
*The graphics looking better and less cartoony in Civ3 than Civ4.
*The fact that I bought Civ4 at launch. This resulted in trying to play the slow, inefficient Civ4 1.00 on a slow, inefficient computer with inadequate resources for it. This didn't help the "epic" element, either, although even with adequate hardware now I find Civ4 is much less epic than Civ3. I'm now venturing into Civ4: Warlords a bit, but have yet to have much desire to try Beyond the Sword.
Probably one or two other reasons that I'm forgetting. As for Civ5, reading about it here has persuaded me that I shouldn't buy it now due to a poor AI, many bugs, and having even less of an epic sense than Civ4 at this stage, and the demo didn't change that conclusion - it actually reinforced the poor AI part. It seems there's not much of a reason to buy it, even if one-unit-per-tile would work if the AI were decent. I figure by waiting until it's patched up/expansionized to buy it, I'm much more likely to have a positive view of it in the long term.
2010 probably is the year in which I've played the least Civ3, other than 2006 when I played Civ4, since I bought Civ3, though. OTOH I've probably spent the most time on Civ3 modding-related activity of any year since buying Civ3, and my Civ4 playing time has remained quite low for three years running now.