Sisko. And he’d do it Hawk style. "Pee-card (grin). Gonna take your head off, 24/7! We’re rOLLin’ now! (that little hiss he does “Hhhhhssss!)”
I think Picard’s a lot tougher than y’all are remembering. In addition to the Klingon battles mentioned above, he took out a bunch of terrorists in “Starship Mine.” He fought through his Borg implants. He survived and withstood daily torture from a sadistic Cardassian. And dude successfully evaded hooking up with Lwaxana, so he’s aces as a strategist too.
Never underestimate wiles and endurance in a fight. I think Kirk would start out strong but Picard would end up fucking his shit up but good.
Lest we forget, Kirk has already been faced with such a challenge against another starship captain. Within a matter of hours, he managed to construct a functioning bazooka out of dirt and weeds.
On the other hand, Picard-- despite all his training, experience, and the resources available to him as a starship captain-- never even managed to exploit a single opportunity to kill Wesley Crusher.
It wouldn’t even be a close contest. Picard would be Elmer Fudd to Kirk’s Bugs Bunny.
“Kirk! There’s no sense hiding inside that cave! I should warn you, I was quite the fencer back at the Academy! I’ve fashioned myself a crude rapier out of a stick and another stick. You’ve no hope of victory! Listen to me: if you will only surrender, as reasonable men, I feel sure that we can negotiate a mutually–”
GIANT SPRING-LOADED BOXING GLOVE EMERGES FROM CAVE, PUNCHING PICARD INTO GEOSYNCHRONOUS ORBIT
Picard would surrender. Naturally.
400 quatloos on the newcomer!
Wow, I am surprised at how little faith there is in Picard. So far the totals are…
Picard: 3
Kirk: 11
Sisko(?): 1
Humanity: 1
I am so disappointed. I think I need to re-evaluate my life.
Hello? 1989?
Jesus…next thing you know, the Lakers will be playing the Celtics in the playoffs, American Gladiators will be back on TV, and we’ll have a new Indiana Jones movie.
:rolleyes:
Picard would attempt to negotiate. Kirk would pretend to negotiate and use the distraction to get within striking range. Then he’d stab Picard in the throat. All over from there.
Maybe you need to re-evaluate your user name.
Oh what the hell. Another vote for Kirk. He will fight dirtier if needed. He would cheat if needed. He should win the straight physical battle as he is a seasoned brawler.
Sadly and inexplicably, Grudge-Match failed to do this match. Probably as it was already an old argument by the time the WWW got going. Here are their other Trek related matches: Star Trek Humor @ WWWF Grudge Match
Kirk, like Cool Hand Luke, he won’t stay down.
The Lone Gunmen settled this question a while back.
(I put in another vote for Sisko!)
Janeway would kick both of their asses.
Results on Googlefight :
Captain Picard 356,000 results
Captain Kirk 1,400,000 results
[sub]Like there was any doubt.[/sub]
Kirk would not hesitate to kick, bite, pull hair, (if it was applicable) or eye-gouge.
Kirk wins in a walk.
How about Ron Tracey, he almost whipped Kirks ass.
Almost only counts in horseshoes and compression phaser rifles. 
Kirk, duh. Kobayashi Maru.
Kirk wins even when it’s impossible for Kirk to win.
Star Trek III. “I have HAD! ENOUGH! of YOU!”
Kirk, no question. Picard only wins his fights because the 24th-century has become so pussified that having even a balsa-wood spine ensures victory.
Damn you. I almost choked laughing at that! 
True. Remember, Kirk was determined to start a nuclear war on 2 planets in his diplomacy.
He punched a guy made out of rock once, too. He’s got some brass ones on 'im.