No doubt it is Alabama. Who cared about Florida until Spurrier got there? The rivalry with Alabama goes back a looooooooong way.
And I am not sure I get the "older people" think the Bama rivalry is better. I am 25 years old, and i hate Alabama with a white hot hatred. Even in elementary school, I hated them because we could never beat them.
I am sure that regionally it matters. I hail from Lynchburg, TN, just half an hour from the Bammer line. I went to college in Huntsville, AL. That made my hatred worse. Now I am in Birmingham, and you can imagine how I feel about them. I understand those from GA or FL hating the Bulldogs or Gators more.
If you think the Bammer fans think that Auburn/Bama is the bigger rivalry, then you have a point on some level. It is about perspective...there are more Auburn fans in their backyard than Tennessee fans. Part of the Bammer thing is that by acknowledging UT as a bigger rival, they know they give some type of credibility to UT, and they will not do that. I GUARANTEE you that if you ask any Bammer fan who they hate more: the Vols.
Go read the book Third Saturday In October. You have to understand the history! You won't even get ten pages into it before you acknowledge without a doubt that the Tennessee/Alabama game is the best that college football has to offer.