I've never been to either, much less stayed at either.
I have a theory, though, and it has nothing to do with whether one resort is truly better than the other:
CSR's theming suggests a place that is much farther away, and much more different in appearance, weather, etc. than CBR is from Orlando.
While some of the locales being imitated by CBR are often less than 500-750 miles away or so by air, with similar weather to Orlando, CSR's locales are much, much farther away and reflect much more different cultures, weather, and appearances than CBR does.
By the same token, and assuming the same kind of quality in both resorts (I know, not a safe assumption), CBR would probably do much better if it were built at
Disneyland than CSR would do, due to Disneyland's much closer proximity to southwestern areas than to Caribbean areas.
I think people enjoy Disney's ability to make it seem like you are somewhere rather than just in central Florida. CBR doesn't provide that as much as CSR does, especially when you consider you can hop in a small plane at MCO, or even a GA airport, and be in a real Caribbean location in a very short time. It's not so easy or quick to get to southwestern areas from there.