Flip a coin...we have stayed at both resorts and enjoyed both.
If you like the Caribbean theme, with pastel buildings, beaches, and steel drum music, CBR might be for you. But if you prefer the old south antebellum/rustic atmosphere, POR is your ticket.
Grounds are spectacular at both.
POR has a better food court, but CBR has been recently refurbed.
Rooms at CBR are a bit bigger that POR's.
POR has a bit bigger gift shop, a much bigger arcade, and an indoor bar area with entertainment, if these things matter to your group.
POR has the boat service to DTD, which is a nice feature.
Check-in area at CBR is in a separate building, quite a hike from Old Port Royale (main building with food court, gift shops, etc.). Could never quite figure out why Disney did that. So POR's main building gets the nod for having everything under one roof.
POR has a sister hotel that is only about a seven minute walk away. A great place for a stroll...try the food court for lunch, look at the beautiful New Orleans themeing. Guests at POR can use the pool and hot tub at the French Quarter too.
Bus service at both we found about equal.
I guess I would give the edge to POR but not by much.
Whichever you choose, you will have a great time.