I was one of those that was "alerted" to this poll at the Civ 3 forums. So I came-and voted for Civ 2. Civ 3's flaws are irreconcilable with me, and severly outweigh its benefits.
To illustrate, I will begin by digesting Mr. Dadoo's comments:
1) The AI seems better now, but you haven't had as much practice with it as you have had with the Civ 2 version. If the situation was reversed, we would probably claim that the "new" (in this example, Civ 2) AI was still more challenging.
2) When you're right, you're right. Visible borders are a plus for Civ 3, as is the culture system (something to focus on rather than warmongering).
3) I couldn't disagree more. The new trade system is unrealistic; the new spy system, incredibly boring. When in real life has most trade been handled by diplomats?? For millennia, it has been individual entrepreneurs and corporations that have created trade, not government. In fact, these groups often led to great achievments independent of governments. Example: the joint-stock trading companies in 17th-century England, the Netherlands, France, and other nations sent forth numerous expiditions responsible for the charting of much of the Americas, the establishment of multiple colonies and factories (ex.: Quebec, New Amsterdam [now New York], British India [oddly enough started by two shipwreck survivors], etc.)
And as for espionage models? What's more exciting, a cascading-window-based, overpriced and often detected buffoon suggesting the image of a disgruntled cubicle-dwelling government worker
, or a kickass-covert operative-Tom Clancy-ish ninja

or studly 00 agent with a license to kill that would make Ian Fleming proud?
4)I
do like the new bombardment ability (though I was able to duplicate a limited version of this in Civ 2 long before Civ 3 hit the shelves), although I think airplanes should be given lethal bombard vs. ships
standard, as it's ridiculous to think that my bombers can't sink a barbarian galley that I somehow missed w/my destroyers' 8 inch shells... Better make ships have lethal bombard against each other as well.
Need I go on?