"Brave New World" adds a lot of new mechanics that make the game more complex in some areas, more varied in other areas and overall more balanced. It adds a religion system that is fun to use (technically added in the "Gods and Kings" expansion, but you get it in Brave New World too), completely redoes how the culture victory works, adds more different types of technologies and also changes how trade routes work. I think it also changes a few of the bonuses that different Civs have to make them more fun to play.

I tried playing the base game after playing Brave New World. There is no comparison. The base game is nowhere near as fun, nor is it as interesting. It's still a fun enough game on it's own, but it goes from an "ok" game to a "10/10" game with Brave New World.