I love 'Rainbow Connection', it was one of my first solos, and I still remember standing on a stage in the eighth grade in a rainbow colored dress singing it. So, yes, the somg evokes great memories for me.
Of course the song that really shows Kermit is probably 'Bein' Green', just because the lyrics pass to him. I think that for his anthem, I would have to pick that one, but overall as far as which of the two I like, I'd select 'Rainbow Connection'.