Wow I'm shocked Sisko is neck and neck..he's not really ranked that high in popularity polls. He's also the captain from "In the Pale Moonlight" and his relationship with the wormhole aliens and the Bajoran religion would lead me not to trust him very much. Early in his appearance on the show it was a different issue...the Borg and loss of his wife that made him suspect..since he treated a fellow officer rather poorly about it. He also sulked about his command of DS9! Yeah, not really a good first choice.
I'd have to choose Picard...he has the right balance of leadership skills, diplomacy, and military know-how to get the job done. He also has a finely honed sense of morality and justice..not above breaking the rules if necessary, but he doesn't flaunt them like Kirk.