I hope the new pope is a little less tightassed about gay rights and condoms.
Alas, I think this is unlikely, as much as I wish it were so.
The Catholic Church's biggest following right now is in Africa, and several of the top candidates for the White Dress and Red Pumps are from African churches, which as a general rule hold to the "traditional" (read: dark ages) opinions on such matters even more fiercely than European Catholics.
Meanwhile, if the church were to choose another European pope to lead the show (jazz hands!) in an attempt to appear less draconian, they offend where their largest remaining power base is.