Even though I saw the new movie first, I had a really hard time with Kirk. Not trying to flame anyone or anything, but I disliked him very much, to be honest. He's grown on me through reading discussions about him (and, well, he is a rather pretty thing

), but I came away from the theater seeing him as very arrogant and undeserving of the promotions he received.
It confused me very much based on what I had been told about Kirk from people who admired him. I just didn't see that leadership and benevolence for which I was looking. When I watched TOS, however, I quickly grew to love Kirk. Though Spock remains my favorite character, TOS Kirk is a captain I could happily follow. He's confident without being too cocky, he's smooth, he knows when to charge and when to play it level-headed.
Pine's Kirk just seemed out-of-control to me. I'm assuming now it's because the movie starts before Kirk is captain and, of course, he must grow into the role. I like Pine and hope to see a slightly more mature Kirk in the next movie as he continues to handle the responsibility of leading the Enterprise crew.
As many people mentioned already, the moment where I started to "buy it" was at the very end, when Kirk strides onto the bridge-- in particular, when he accepted Spock as first officer.