Civilization IV represents a HUGE leap forward in the series.  With Civilization III, there were some new features, but anyone who had played previous Civ games could pretty much just jump right in and feel comfortable.  That's still true with Civilization IV, but there are so many new features that the game is very different from its predecessors.

 Civilization IV adds tons of new features and content such as the social engineering found in Alpha Centauri and completely new concepts such as state religion.  The game also takes the complex diplomacy that Civ III borrowed from Alpha Centauri...