Big East, hands down - while the AAC has consistently had 3-4 good teams, the Big East was strong top to bottom - with the exception of Syracuse, most teams had a winning record at some point.
In 2006, 6 of the 8 teams went to bowl games (75% of the league), with Louisville winning the Orange Bowl over Wake Forrest and 3 teams finishing in the top 15. 2007 featured WVU beating #4 Oklahoma in the Fiesta Bowl (from ‘05 to ‘11, the Big East pretty much had 5-6 teams a year in bowl games)
The best AAC season was probably 2017, where 7 of 12 teams went to bowl games (58%), with UCF winning the Peach Bowl over #7 Auburn and 3 teams finishing in the top 25