Nine of the eleven Big East schools are Catholic. Butler (founded by the Disciples of Christ) is now nonsectarian. Only UConn is a public flagship state land-grant university. We have nothing in common with the rest of the league other than (some) geography and a modicum of historical rivalries.
While the geographic challenges (including cost) of travel to Big12 opponents are real, UConn is a much better fit. And please don't take a Northeastern arrogant stance that "flyover country" is beneath us. I served two tours of duty in Oklahoma. Wonderful, friendly, welcoming people who, by the way, care deeply about the USA. Yes, most don't go to Harvard, Yale, Middlebury, Amherst, Williams, etc. High schoolers there actually look forward to being admitted to their flagship state universities.
I, UConn (BS) and Harvard (MBA), heartily embrace a potential move to the Big12.