I can't ascribe much character to Civ V because it's just gradeschool caricatures of history. It was better before V, but if V is their template of storytelling and character, we're utterly fucked.
I don't see though how it was better before, Civ has never been about history per se. What defines character in a 4x game to me is art style, factions and lore.
Civ V has a clear art style, unlike many other Civ games.
Civ V has very unique factions, that actually feels like they play extremely differently depending on their historical context, also the leader animations are a nice addition.
The lore is history, like all other Civ games...
You can say what you will about the gameplay, but really I do feel that Civ V really has a unique feel, so much so that many newer 4x games try to copy Civ V when it comes to the feel and character (age of wonders III, Warlock I + II).