How do you figure the CYO is a better basketball conference? Or is your definition of better just that we have played them more?
Let's imagine they add programs like Xavier, Butler, and one other than has had recent success (VCU? Creighton?)
Since 2000, UConn has been to the Final Four 3x, and won 2 titles.
Cincy has done nothing in the post-season (2 S16s)
Temple has done nothing in the post season (1 E8)
Memphis has a vacated FF, and some other nice runs. All with Calipari, who is no longer there.
USF (1 NCAA appearance), UCF (2x from the A-Sun), Houston (1x), SMU (0x), Tulane (0x)?
None of those schools are as good as PC, DePaul, or Seton Hall. Seton Hall has gone to the NCAAs 3x in that time (not good), but was in the mix more. And that's 1 less than all those other schools combined. Providence only 2x. DePaul only twice as well. But their better programs than all the bottom-feeders in the NBE.
Marquette, Georgetown, and Villanova are a step down from UConn, but are an improvement over Cincy. Each has been to a Final Four in the last decade. You add Butler, they have multiple appearances and two Final Fours. You add Xavier: they haven't missed the NCAAs since 2005, and 2 E8s and 3 S16s in that time.
The worst programs in the CYO are better than the worse programs of the newcomers. Generally by a lot.
The only program in the football schools left that is as good as the best CYO schools is UConn. Memphis and Cincy are a step down. Anyone else you add is a step down, especially once you assume they're going to add schools that have basketball success in their recent history.
If SDSU comes for basketball, and we add another western school with some semblance of basketball history (UNLV?), then a top group of UConn-Cincy-Memphis-Temple-SDSU-UNLV can rival a top of GTown-Villanova-Marquette-Butler-VCU-Xavier. But they'll have more Final Fours in the last 15 years than ours, and a deeper history.