Kirk seems to have had more hand-to-hand combat scenes on screen, but I would still say Picard - based solely on the fact that he had been in Starfleet for 52 years by the time of Nemesis.
What about Janeway?
22.214.171.124 04:42, July 6, 2011 (UTC) I think sisko might, he got into a lot of fights with cardassians
Picard is a trained fencer. While that's not worth much in real combat, it's still a history of hand to hand combat experience, which there's no evidence that any of the other captains had.
Although he was going slightly crazy at the time, according to Riker in a TNG episode, the TNG hand phasers can obliterate an entire wall of a building on the wide beam setting. Picard doesn't need combat experience, he just needs Commander Riker's phaser and he'd be fine just firing it randomly in the direction of the enemy.
I still have to go for Kirk, closely followed by Sisko, then Archer, then Janeway, then Picard, After all Kirk had atleast one good fight in all his adventures, Sisko broke any enemy that got in his way including several klingons, Archer defeated a borg, a vulcan (which neither of the previous two managed) and that cowboy, even with shot gun pellets in his shoulder.
Picard was a diplomat, he only got into hand to hand combat about twice, as far as I can rember, there was that fight with his brother, which ended with them laughting and drinking together, and that daft looking one with the nausicaans, and just because he spent all that time as on a ship, dosen't mean he was more experianced to fight, it just means he had more experiance on board a ship.