I fit the demographic of someone who "loves Civ3 and [at least before BTS] disliked Civ4". I don't know if I'll end up loving Civ5, but having actually tried it now, I think it's a better game in the vanilla version than Civ4 was. Of course, it probably helps than I'm not trying to run it on a mid-range Pentium 4, so it doesn't run super-slowly, but I think it's probably better overall. It might also help that expectations were reset after Civ4.
I think part of what I disliked about Civ4 was that it was a smaller scale, and some of the combat options (such as artillery) weren't as good. Civ5 is still on a smaller scale, but the way artillery works makes sense. I think it's also clearer that Civ5 isn't trying to be quite the same game as Civ3.
There's also, IMO, better new concepts in Civ5 compared to vanilla Civ4. Civ4 introduced religion, which could be OK, but made diplomacy a pain. And Civics, which I don't think were a big step up over Civ3's governments in practice. Whereas Civ5's policies seem to actually matter in terms of the direction of the game. City states are an interesting new dynamic, although perhaps a bit too much of a gold sink. The hex grid seems to actually work fairly well, and I'd say was a better swap than isometric for square in Civ4. The happiness concept still doesn't really make sense realistically, but that both serves to make the game distinct from Civ3, and it does a good job of making happiness important. And, I kind of like the expansion concept of expanding tile-by-tile rather than in whole levels. It makes the growth feel more organic.
In terms of doing what Civ3 does better than Civ3, I don't think Civ5 can do it (at least without major mods to happiness, 1 UPT, and map size, and perhaps a few others). But unlike Civ4, it doesn't seem like that's the obvious goal.
I disagree that 1 UPT is appealing to Civ3 fans, though. Unless possibly as an alternative. True, it does allow blocking, but Civ3 is the king of stacks of doom.