Alabama wins hands down, reasons: When the league expanded and split into divisions in 92, there were a lot of old rivalries that had to take a back seat due to the new alignments. We used to play a 5/2 round robin. In other words, we had 5 teams we played every year and 2 that would rotate on and off from among the other 4. We played annually: Vandy, Kentucky, Bama, Mississippi, Auburn, and the other 4 teams bounced on and off the schedule. Prior to 1988 the SEC only played 6 conference games and the round robin was a 5/1, whereas; 5 teams were on the schedule annually and the other 4 bounced on and off to make up the 6th game.
Prior to the SEC's division and expansion, Georgia Tech rivaled Alabama as our greatest rival. Tech was a member of the SEC until 1964 when they went Independent, then later joined the ACC. Even after Tech left the conference, we were such bitter rivals that neither school could bear the thought of not playing, so they remained on our schedule for another 23 years. From 1954 until 1986 we played them every year.
When the conference went to division play, it meant you played every team in your division and 3 which were not in the division, but with the only logical way to split the conference was by geography, it meant some of each team's annual rivals had to go. This was a real dilemma for the conference. For instance; one of Georgia's greatest rivals was Auburn, so the conference came up with a format that allowed 5 divisional games, 1 non-divisional but annual game (We got to keep Alabama) and then the other 5 teams bounce on and off to make up the other 2 conference games each year.
I can assure you that if Alabama/Tennessee had not been salvaged, there would never have been an expansion with divisional play.
So my vote goes to Alabama.
Now, you can argue this decade, the last 20 years, the last 5 years, but to all of the old-time Vol fans it is and will always be Alabama.