Hey guys, I'm just jumping into this now, so I apologize if anyone has made the points I'm about to.
Both could be considered a Kermit theme, but....
Bein' Green is more specific to Kermit. The lyrics are slow and mellow, much like Kermit. It shows how even in circumstances that seem dark or negative, you can always turn things around and look positively, if you choose to. To borrow the term, "Life's a Happy Song" if you make i that way, which is how Kermit sees the world.
While, Rainbow Connection is definitely a Kermit song, it is also more broad to be a Muppet Song in general. It was used as a reprise in The Muppet Movie, and sung as a duet (and later ensemble) in The Muppets. It's a song about rising up, and chasing your dreams, about never giving up. This is something that describes the Muppets in general, because no one can keep them down, Not Doc Hopper, Not Nicky Holiday, and Not Tex Richman.