I think Pike as played by Hunter came across as a more restrained and introspective character than Shatner's Kirk. However, I do think that this had as much to do with the style of acting as the writing. I don't really think the characters were written massively differently, at least, S1 Kirk wasn't.
The way Kirk was written definitely changed over time, and in his first several episodes, he was very much like Pike. In "The Corbomite Maneuver," he had the same discomfort toward having a female yeoman that Pike had. And in "Mudd's Women," Kirk was the only human male crewmember who wasn't gaga over the women, because he was just so darn serious and driven and committed to his duties. That's hard to reconcile with our eventual image of Kirk the womanizer, but it's something that would've felt perfectly natural for Pike if Hunter had remained the series lead.