It depends on what I'm in the mood for, I suppose. I like pretty much all of the various types at various times.
The Batman type, though, is probably my favorite. Good enough to do all the impossible things we like fictional heroes to do, but doing so with the full knowledge that a lucky mook with a Saturday Night Special can kill him instantly.
Of course, it all depends on the writers. I lost interest in 'Batman the Psychopath' when lazy cheap writers who'd read too much into their Psi 101 text books started going down that route. More and more, they've pulled away from that lately. (Of course, the best Batman in recent times to me was the two years or so Dick Grayson was under that hood.