I'm a vet of the whole Sid Meier 4X series of games.
I much prefer Civ III to Civ II.
I find the emphasis on diplomacy is good. The presence of strategic resources is important now, so are the luxuries for that matter. There's a lot else here that pleases me as well.
The only weak point for me is in the espionage functions. They're all inferior to Civ II in my opinion. I like the theory of "no-spies" and doing it all from a large screen, but the implementation is weak. Everything except for investigating a single city is just way to expensive to ever be worth doing.