Using total attendance numbers to compare fan support is not a true reflection of actual support. Thompson-Boling seats nearly 6300 more people than Coleman Coliseum. Even if Bama sold out every home game, and Tennessee was at 80% capacity, we would have a higher total attendance, but which team is being supported more?
Historically, Tennessee has had greater fan support than Alabama has in basketball, in spite of the fact that Alabama actually has a pretty good basketball history (2nd most total wins among SEC teams). Tennessee is right on their heels, in 3rd place, but actually has a higher winning percentage. Both schools each have 17 combined regular season and SEC tournament titles. Tennessee has 23 NCAAT wins, Bama has 22 NCAAT wins, and neither has reached a F4.
Bama football just takes a much deeper hold of the athletic budget, and due to recent success (last 15 years), they get all the fan glory, as well. Basketball has been relatively stale in that same time frame minus the recent uptick. Bama basketball will be much like Florida basketball 15 years ago. If the team gives them a product to invest in, they will do it. Florida won back-to-back titles, and suddenly they are a blue blood in the eyes of some.