It's not exactly the same because Memphis has never been in a top conference and their fans pretty much always feel like they should be. (The AAC losing UConn just after inviting them was probably a Lucy and the football moment.) Memphis has always been a city that thinks of itself as 2/3 not in Tennessee. So all three of Tennessee, Ole Miss, and Arkie are teams they'd like to beat, but not perennial rivals. Maybe Cincinnati feels the same way about not just OSU but also UK, and IU, not sure.
Actually Louisville was a pretty big rival in the Metro conference days (source: my aunt went there) but that's faded into history.
