We've stayed at BC/YC many times and BWI three times. Our boys are currently ages 7, 13 and 14, but we've been taking them to Disney since they were tiny. Our boys love BWI CL, and they have always said that pools at WDW are not a main attraction, just an "extra." So they aren't disappointed when staying at BWI.
As much as I love BWI and will continue to stay there, I'm not a big fan of the clown pool. On one hand, it's far easier to keep an eye on your kids at the clown pool because it's so small and contained. And I do think the slide at the clown pool is the best on WDW property. But because it's smaller and the theme is "circus," it feels more crowded and less relaxing. Stormalong Bay is just more pleasant to look at, and we far prefer the atmosphere and theme there.
On the other hand, the quiet pool at BWI is WONDERFUL! It's entirely relaxing, so quiet, and contains a clean and uncrowded hot tub. It's without question my favorite pool at WDW. We go over to the clown pool at BWI for the kids to slide, but in my opinion, there is no better quiet pool than the one in the BWI courtyard.
We've done a split stay between BC and BWI in the past - we just schedule our pool/slide time at BC and then enjoy quick visits to the quiet pool at BWI. But if you're there for a while, it's worth at least one visit to the clown pool for that fun slide!