re: Bigger Rivalry? Michigan and Ohio State or Auburn and Alabama?

It's all perspective as you say.

Take UGA. rivalries, as a microcosm.
Depending on where you live in the state, the biggest game of the season changes.
North of ATL is generally UT
EAST it has become USC especially in Augusta
West has always been A
In the Atlanta area GT, even though it is usually 1st or 2nd no matter where you live in the state. Macon south is all about the WLOCP, always will be.

So even though the Iron bowl is a great rivalry, the importance changes depending , the state of Alabama basically closes for the game, it's must watch for those in the west, in east it matters but not as much and the channel will change for other games. Nationally , people watch , but it's usually not first choice unless nothing else on matters to you .