We love both!
Caribbean Beach is more spread out, older, and can be difficult to navigate. But people also say that about POP.
I actually prefer POP to the moderates. But given the choice between the two, if you can afford it, go with CBR!
Disney hotels are NOT noisy. I find a lot of the time that it's Americans who complain about the noise! As long as you don't go during any cheerleading conventions and stay in a budget resort you should be fine. If you're going off season, POP is fine, but if you're going at a busy time maybe CBR would be better.
Arg it's a toss up, I genuinely do love them both, but I think CBR has the advantage due to it having it's own restaurant (POP only has a food court, CBR has both), a main themed pool with a slide and several quiet pools (POP has only big pools, no slides), a much nicer walk around the grounds, and nice bus stops. The bus service at POP tends to be better though. So I guess it depends on what you're looking for!