Old Kirk or young Kirk? Old Kirk is doughy and he would be pretty evenly matched with Picard. Young Kirk would clean his clock.
Against Young Kirk it wouldn't even be interesting. You might as well toss Picard into a giant blender and see how he fares. Young Kirk would settle it with a single judo chop or maybe one of those hands-clasped double haymakers. He wouldn't have to pull his signature move, The Thing Where He Jumps In the Air and Kicks With Both Feet (TTWHJITAAKWBF). The only creature who can resist that is a Gorn.
Old, flabby Kirk would still prevail because, well, he's Kirk. But it might be interesting if Picard tries to confuse him by talking with that sissy accent.