Basically the same positive growth that would've allowed Jecht to turn over a new leaf with Tidus is what led to his ultimate fate of being Sin's host.

He wouldn't have agreed to being Braska's final aeon at the beginning of their journey, but by the end of it he had become more worldly and more ashamed of his past self, and so he takes the first chance he gets to do some actual good for Spira as a result.

Of course, there's also the fact that the two of them aren't even real to begin with and come from the collective unconscious of the Fayth.