I find it's a tough call between Picard and Kirk.
Whilst Picard would be a better Captain and a fairer boss, I can't help but feel the atmosphere of his Enterprise is more elitist, and unless I was a high ranking Officer, I wouldn't get to personally experience any of the Picard goodness.
I'd just be a nameless nobody, fading into obscurity and a bottle of Romulan Ale in Ten-Forward, making a nuisance of myself by pestering Guinan to tell me space jokes, and trying to get Data to tell Worf 'blue' Bernard Manning type jokes, or call him archaic racist names, which would be be hilarious to me because neither of them would get it (
Data, next time you see Worf, greet him with "Yo Dawg! 'Sup my ******!").
The Holodecks are a big attraction to serving under Picard, but they'll probably always be booked by Picard and his Officers, playing detectives and whatnot, plus I'd probably have my few Holodeck privileges revoked for being a drunk and trolling the robot.
On the other hand, despite the shittier technology and much greater risk of death, Kirk's Enterprise just seems a lot more fun, plus he had much better adventures, as this brilliant Youtube video highlights.
Yes, definitely Kirk, it would just be so totally surreal (actually serving on a 60's Technicolor starship), plus it would probably be constant 'shits & giggles' right up until I get eaten by some alien tree monster or something equally ridiculous.
Even then I'd get a kick out of my absurd demise, because unlike in Picard's elitist, hard working TNG era, I actually think I'd have half a chance of being a half-assed TOS crewman and becoming involved in some of Kirk's wacky adventures, even if I was just a Red Shirt.