I cancelled my cable years ago so I've only seen their shows in bits and pieces on youtube. Fallon's more talented (especially musically) but he's soft as pudding in interviews, almost "Entertainment Tonight" with his fawning. Kimmel has a bit more of an edge, from what I've seen. If I were forced to watch an entire episode of one, I guess I'd say Kimmel.
Neither is close to Letterman in his prime (i.e., the 12:30 a.m. NBC years).
As for Carson, I always thought he was overrated. The monologues were good, the interviews could be pretty good, too (unlike Fallon and Kimmel, he seemed well-read, at least by the standards of TV), but the comedy bits were mostly lame: Carnac, the redneck with the hunter's cap, etc. Plus, Ed McMahon really grossed me out. Was he necessary? Even Carson didn't seem to like him.