I grew up in LA, went to undergrad in Chicago, and worked in SF for 4 years before moving back to LA. I also prefer LA, by a lot. Though, having grown up here, I'm clearly biased. Still, re: some of your concerns:
Sprawl: LA covers more landmass, but the attractions of each neighborhood are fairly compact. The "city-centers" of Santa Monica and Pasadena, for example, are very walkable, and although I've never taken public transportation in LA, I have friends who commute via Metrolink (train) and they seem to like it.
Traffic: Terrible. Soul-crushing in west LA.
General culture: Here I think the sprawl works in LA's favor. There are so many really different neighborhoods, it's pretty easy to find somewhere that fits your interests (except for theater. There are some nice playhouses but the theater scene here doesn't compare to Chicago/New York). And, aside from the traffic in Santa Monica, I agree with everything MAB1980 said =).
P.S. That said, I've visited SC a bunch of times (both for the MPP program and to see friends who went there), and I'm not keen on that area.