Let's see. "How a captain deals with death is at least as important as how he deals with life." Let's take that and run with it.
Picard. One of his closest friends and primary crew members die. He sees a tiny hint that his friend's essence might have been stored in another body. He is overcome with hope to one day see his friend again.
Kirk. One of his closest friends and primary crew members die. He sees a tiny hint that his friend's essence might have been stored in another body. He steals a starship from Starfleet, sabotages the pursuing vessel, travels to a forbidden planet, kills some klingons, obtains the body of his friend, finds a way to bring his friend back to life, then, while on his way home, stops off in the twentieth century, saves the world, then comes home to get punished by getting a brand new starship to command.
Sisko, no contest. Though Abrahms Kirk has potential.
Why Sisko? Four words: In The Pale Moonlight.
Kirk was brash, cocky, and impulsive, but when push came to shove he was still the upstanding moral paragon Starfleet likes to think it is.
Picard had his moments ("THERE ARE FOUR LIGHTS!") but overall pretty boring.
Janeway was... god, don't even get me started.
Archer wasn't bad, but a bit too idealistic for my tastes.
Sisko could hold his own in a fight, and wasn't afraid to do so (I mean, he decked Q! You wanna talk about cohones of carbomite...), had considerable tactical acumen (being a major planner of strategy during the Dominion War), an excellent diplomat when called for (just watch any situation where he's bowing out of Emmissary duty), and when push comes to shove, he can toss every moral he has out the airlock to do what needs to be done for the greater good of the Federation and the Alpha Quadrant.