I'm not sure it's fair to say that Peyton identifies more with Tennessee. He is loyal to his college team, but both Peyton and Eli worked to get supplies to New Orleans and have supported recovery efforts for their hometown. I doubt that anyone here actually how Peyton identifies himself.
They were both born and raised in New Orleans. This thread is reminding me of that old joke, that in New Orleans, the Welcome Wagon calls on you until the third generation. The idea that someone born and raised in New Orleans isn't really from New Orleans is one that has kept the city isolated from new businesses--and this was before Katrina. Corporations did not want to locate there because their top managers could not be accepted into New Orleans society. New Orleans was isolated from new money coming into the city, and it's one of the reasons that it stayed so poor.
New Orleans needs help from everyone to recover from Katrina, including "outsiders" who were only born there to parents who were born elsewhere. Maybe it's time to let this attitude go.