I have stayed at both and I have my obvious favorite, hence my name.
The bc pool is awesome. My 3 year old could spend all day in the gigantic sandy pool. The super deep lazy river and slide were perfect for my 9 year and my 5 year old bounced all over the place. If I had been a single parent with 2 or more kids with differing swim abilities there is no way I could have handled this pool! But with 2 parents we were able to keep up and had lots of fun. Hurricane Hannah's was great for lunch and drinks. The marketplace was convenient if crowded. I had many a flatbread pizza there.
Breakfast can be had at the marketplace or the captains grille over at the yacht club. There's a character breakfast at cape may cafe, but probably would require adrs. Good coffee can also be had in the lobby lounge of the yacht club.
And now for why I like the BWI more. It is quiet, beautiful, peaceful. The quiet pool is actually quiet. The clown pool is manageable for parents! Leaping libations serves the best margaritas. The rooms are beautiful. The lobby and lounge are dreams come true. The music, the gardens, the staff, I could go on and on.
Breakfast at the BWI is serviceable, but then we are not big breakfast people. If we stay concierge, we're fine with yogurt, HB eggs, fruit, coffee. If not concierge I love walking down to the belle vue lounge for danish, coffee and fruit. The bakery has recently been expanded since I've stayed here, so I can't comment.
Bottom line, if you have kids who LOVE to swim and you can handle it. If you don't require quiet ANYWHERE. If you want the quickest possible walk to Epcot. Go with BC.
If you really need a place away from the parks and people that is peaceful and beautiful. If you want a fun (but not amazing) pool or a truly quiet pool. If you want to walk to Epcot and DHS. Go with BWI.