They were a national contender in basketball in the Big East but have struggled to replicate that success in the AAC. My guess is they hope that rejoining the Big East will help make them nationally relevant in basketball again.
BYU used to be relevant in football as part of the best G5 conference (used to be the MWC). Joining the AAC (currently the best G5 conference) would perhaps help BYU replicate their past success as well.