As shown in the following diagram, the remaining Big East schools (and some set to join) will be splitting into two conferences. Shown in blue are what had been widely referred to as the "Catholic 7" (some of the Big East's longest-term members, whose athletic programs are focused on basketball), plus like-minded schools Creighton, Xavier, and Butler, who will be coming on board (Butler is private, like the other schools, but not Catholic-affiliated). This group will retain the name Big East.
Schools in the new AAC play football in the NCAA's top classification (known as the Football Bowl Subdivision and formerly Division I-A) and have enjoyed various degrees of success on the gridiron. None of them would be considered among college football's elite, however.
I see the new Big East as being very stable, as it essentially is a new incarnation of a league that has been around since 1979, with a similar culture as the original.
In contrast, I would be very surprised if the American Athletic looked the same in five years as it does today. In general, circuits with large geographic distances between members have tended to be volatile. UConn and Cincinnati have been known to covet membership in the Atlantic Coast Conference. Further, though it may not currently seem likely, the two Texas schools, Southern Methodist (Dallas) and the University of Houston, conceivably could find themselves in the Big 12 (which currently has 10 institutions). U-of-H is building a new football stadium, which can only help the Cougars' prospects for joining the Big 12.