Shogun 2 is AI-wise, performance-wise, general aesthetics-wise and UI funtionality-wise miles ahead.
The only downside some people have about it is that the game is too narrow in scope. Which I guess is a valid complaint. However, I really like all three campaign. Fall of the Samurai especially is fantastic.
EDIT: Oh, it also has bunch of features that I really love. LIke a god damn family tree. They really overhyped the Rome 2 internal politics shit.