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.
If you like diplomacy and trade, Civ III. If you like combat more, I would definitely say the Ctp series. It probably depends upon which areas of gameplay appeal most to you. 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.