To the Pats*, Buffalo is the game where you can get cheap tickets.
To the Dolphins, Buffalo is the 2 winnable games on the schedule
To the Jets, Buffalo is the guaranteed 2 wins, and also the team that guarantees NE 2 wins, too. So at least the Bills get under the Jets' skin at least a little bit.
Buffalo doesnt have a rivalry. Teams that suck don't get to have rivalries. Hopefully this changes soon.