The UT-Bama rivalry has always meant more for me until recently.
Depending on which side of the country you live in, people will view rivalries differently. Out here, people view the UCLA-USC rivalry as the biggest. If not that, Michigan-Ohio State. The Iron Bowl meant a lot to me when I was growing up in Alabama, but not so much anymore because I don't have to deal with those obnoxious try-hard rednecks that want to be Alabama. But nonetheless, it is a big rivalry. Outside of the military games, I'd say it still ranks like this nationally:
1) "The Game" 2) The Iron Bowl 3) Red River Rivalry
Some very underrated rivalries ( or at least in my opinion) that need more nation attention because of its intensity and hatred: 1)Clemson-South Carolina 2) Oregon-Washington 3) Alabama-Tennessee (though a big rivalry, has lost its luster)