For me:
civ 4 has religions, corporations, better espionage system, a lot of unique units and buildings, un resolutions, apostolic palace, a ton of promotion options, great people, a balanced combat system, wonders you can actually see on your cities--and wonders that actually are worth building, a cool city screen, smarter automation, easier unit cycling and management, kick ass music, modding friendly xml, a lot of civics options, solid gameplay (no game breaking abuses), great graphics and animations, a plethora of random events, a nice and helpful user interface (even better with the BUG mod), bombers and stealth planes no longer base on carriers (as in real life), a killer globe view of the world, a non-linear tech tree (you can now skip techs and still enter a new era), built in music player, offers a variety of strategic and tactical options and more...
civ 3 has the nostalgia factor having played it for four years in college, simple graphics that is not so heavy on the computer, an abusable infinite city sprawl tactic, leaders that change dresses according to eras, stacks of doom, the breaking border agreement/ROP abuse for quick attacks, armies (modern armor armies ftw) and animated and funny advisors.
your call.