In the new Big East, I consider St. John’s our most natural rival with PC a close second.
Proximity is the most important factor.
Both typically field competitive teams, which is a necessary factor. The years that they are really good, the rivalry becomes hot.
And finally, both their fanbases care about BB, so they bring the hate. You can’t have a true rivalry with a team whose fans don’t get emotionally warped about losing to us.
Seton Hall doesn’t qualify even though they have the proximity factor. Their fanbase isn’t passionate enough about BB, and they aren’t consistently good enough.
Marquette, Xavier, and Creighton can have outstanding teams, like this year. But the consistency of their teams is more up and down, linked to who the coach is. Plus, there’s no local proximity to us. Their fan bases are good, but they don’t project any hate towards us. So none qualify as rivals.
Villanova is somewhere in between. They are usually very good to excellent. And their proximity is close enough to matter. Plus they're a historic basketball school with a good fan base. But they don’t seem to hold any distinct hate towards us as a team or fanbase. There’s mutual respect between programs and fans, but no bitter rivalry.
The rest of the new Big East teams bring no factors to qualify as a rival to us.