In the history of their school, Auburn has won 16 NCAA team championships. 8 in Men's Swimming & Diving and 2 in football, plus 5 in Women's Swimming & Diving & 1 in Women's Outdoor Track & Field.
The University of Florida has won 41 NCAA team championships.
On the men's side we have 1 in baseball, 2 in basketball, 3 in football, 4 in golf, 5 in indoor track & field, 4 in outdoor track & field, 2 in swimming & diving. On the women's side we have 2 in golf, 4 in gymnastics, 1 in indoor track & field, 1 in soccer, 2 in softball, 3 in swimming & diving and 7 in tennis.
Florida has, also, won 242 team regular season SEC championships, more than any other SEC program. Auburn has won 75 SEC regular season championships.
It's not even close which school has the historically better athletic program.