Yes, exactly. Pilots are often more self-contained and TV-movie-like than regular run episodes, and so with "The Cage." Here the central character had kind of a psychological dilemma and didn't know whether he wanted to continue with the life he was leading. After his experiences in the episode, he seems to be more at peace and, of course, ready for more adventures.
When you put it that way, it sounds exactly like "Emissary." If we only knew Benjamin Sisko from the pilot episode, we'd probably think he was a pretty grim, morose figure as well.
And while not as grim or morose as either Pike in The Cage or Sisko in Emissary, I think the Picard of Encounter at Farpoint came across as a slightly nervier, altogether less confident man than the one we came to know and love.
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.
I've read on occasion that NBC wanted a more action-based and less cerebral show than was presented in The Cage. If this is true, I reckon that Shatner was definitely more the leading man for them than Hunter was.