They academically and athletically outrank Nova, so I am pretty sure that means they win.
Nova is not ranked in the National University list because it doesn't confer enough Ph.Ds (Villanov only offers ONE Ph.D, actually), so you cannot make a claim regarding where Villanova ranks in relation to BC, because they aren't grouped together.
Also, BC is in a different Division for football...
In Basketball, however, both teams finished the season un-ranked. Villanova recieved votes in both the AP and USA Today Poll. BC received votes in only the USA Today poll where it had 3 -- Villanova had 7.
Keep struggling to hate Villanova. Be assured that I don't give a damn, I am quite satisfied with the name on my Diploma.