From my take as an outsider, based on what I've seen on these boards I'd rank them this way:
1. Bama - just a long time rival. This seems to be a "True" rivalry game to me. Our equivalent would be the beavs.
2. Vandy - Seems to fit the rival theme as well. This seems more like a hate than a rivalry. Our equivalent would be the puppies.
3. Florida - I don't understand this "rivalry", of course if they weren't in the SEC you'd never see them outside of the state of Florida except for a bowl game. Worst traveling team in the SEC.
4. Georgia - similar to Florida in my opinion. They remind me of UCLA, great "rankings for recruiting" that don't translate to championships very often. Basically, biggest under performers of the two leagues.
5. LSU - Not sure why they aren't higher on Tenn fan lists.
As far as I'm concerned, when I think of the SEC's "storied" programs I think of Bama, LSU and Tenn.