Y’all seem to be forgetting that both Kirk and Picard had hand-to-hand fights with Dr. Soran in “Generations,” so we actually have a good basis of comparison. As I recall, Soran tossed Picard around like a rag doll, but got himself punched out by Kirk – and we’re talking old, pudgy, retired Kirk here, not Kirk in his prime.
There is absolutely no question that Kirk would beat the crap out of Picard if they had to go toe-to-toe. I’m not even sure why people continue to have this debate.
zombie or not, Kirk would try to act serious and say something philosophical and make Picard’s head explode.
My vote is for Kirk.
Both Kirk and Picard could talk their way out of a fight when they wanted to, Picard tended to do it a bit more eloquently. Both have also had their share of fistfights (though Picard rightly delegates that to the Bash Brothers, Worf and Riker).
Now, I might have said this before, but the only way Kirk would clearly win would be if they had to engage in Ham To Ham Combat.
A perfectly logical and irrefutable proof.
I also recall that Soran easily killed Kirk, while Picard was able to shrug off the event. 
Kirk goes all T.J. Hooker on Picard, throws a baton to trip him and such.
If we’re going that route, Picard goes all Professor X on Kirk and leaves Kirk sitting somewhere drooling and singing “Daisy, Daisy” to himself.
Pfft, Professor X can’t hurt Kirk. He lacks the Delta brain wave.
Fine, Gurney Halleck shanks him.
I was going to agree, but we are neglecting the Ripped-Shirt-Kirk. Nothing can stand before HIM. 
I think they’d knock back some Romulan Ale and check out the Green Ladies.
Heck, Gurney could even play a song for the Green Ladies to dance to
…I think we’ve got something here…