The size is fairly comparable I think.
The BCV is tucked in behind the BC so there is no water view available. Of course, you pay more for water view at BC anyway. The other views are comparable IMO although the worst WDW view we've ever had was of the roof at the BC.
A studio will have a queen and a sleeper sofa. BC rooms have too queens (a few rooms have two doubles) and some rooms have a daybed as well. For me this is the biggest difference. Both have a small table and chairs.
There is a kitchenette with a counter, refrigerator, toaster and cabinet in the studios. Not sure if BC still has minibars but the rooms should also have a refrig now I think.
The bathrooms are of the same basic layout as I recall.
If you are using points at the BCV you will not have daily housekeeping service but instead trash and towel on day four and a full cleaning on day 8. If your reservation is through DRC, you will have housekeeping daily.
Some of the rooms at BC are probably a little closer to the lobby. But both resorts sort of fan out from the common areas so there is not a big difference IMO.