Easily Kirk, though I have nothing against Picard.
A couple of things to throw out there. Kirk in the 24th century was genuinely legendary. It says something that Sisko committed a felony just to get his autograph. Picard would have been well respected, but I don't see him commanding the same sense of awe that Kirk did a hundred years later.
Picard got to hide behind regs that prevented him from going on the majority of away missions. If Kirk didn't beam down, it was only because it was to an unpleasant place without any girls. In TNG, Riker got to be the action hero while Picard sat at home and asked him for trip reports.
Kirk was no less skillful in the qualities that make Picard a badass--which he is. Kirk could negotiate with anybody. He could bluff his way out of any situation. He was perfectly willing to blow the Enterprise to bits if the situation called for it. Actually, this is an interesting notion. What is a quality that Picard possesses that Kirk doesn't?
Lastly, I'm sure I can't be the only person who gets annoyed that every single pole or survey here has to have a joke option thrown in to skew the results. I'm cool with Bosk and all, but I'd like to have seen those 8 votes count towards one of the real options.