Well, as someone who does have a lot of experience with both Civ 1 and 2, and Ctp 1 and 2, and who has been playing Civ III much more than I should be in exam season, let me say....
It probably depends upon which areas of gameplay appeal most to you. If you like combat more, I would definitely say the Ctp series. If you like diplomacy and trade, Civ III.
The Civ series has more "warmth" with its smiley faces and busy workers, while Ctp is geared more toward the analytical "engineer" type more concerned with click efficiency (PW and unit stacks) and getting on with the important aspects of growth.
In my games, you spend a much larger percent of your time on big decisions with Ctp, while you spend most of your time moving workers around in the last half of the game with the Civ games. I think that Ctp2 would have been better if the games were a couple hundred turns shorter.
Myself, I have enjoyed playing both games. I think that many here are completely shocked that Civ III is not perfect, in addition to the points Yin and Locutus have made about announced features of Civ III not being included. I kept running into this mentality when people complained about the Ctp series over the last two years, when they would say things like "It just doesn't 'feel right'", with the definition of "right" being Civ 2, or "It's buggy," like all the civ games are flawless, or simply "It seems unbalanced" (which is was), with the insinuation that Civ III will be so perfect that no one will ever think about modding it, but only about making scenarios. (Btw, I don't mess with scenarios because there has never been an AI that can handle the different situations found in a scenario. The only scenarios worth playing in the Conflicts in Civ add-on were the fan-created ones, and those I only played a time or two.)
Bottom line- If you like the new resource and diplomacy model in Civ III, which I love for several reasons, then I would not give up on Civ III until at least the first patch comes out, and we see what the mod-makers here can do with any remaining balance issues.
If, OTOH, you cannot get over the combat inaccuracies and the hassel of moving around dozens of workers, get Ctp 1 or 2 cheap, get the Apolyton Pack for it, or another modpack if you so desire
, and try it out. These games have their flaws and limitations, but as Civ III has shown, all games do.