It's hard to say exactly what the author had in mind here, or even if English was their first language. But I'd take a different interpretation and say that this person feels a little like a different person - a happier person - when in the company of their friend. Specifically "that's more you than me" interpreted as "that's more the way you are as a person than I am".

Probably, the narrator says that in their friendship that "you" person is more important that the narrator himself. The narrator values his friend and appreciate all the things he's done (he makes him smile, cheers him up, etc.). His friend is doing so much and that's why he is "more than" the narrator in terms of their friendship.

The narrator is responding to something the other person said nicely about her. The narrator is saying those nice words you call me, those are you. Check out my teacher profile www.italki.com/teacherhelpme