We've stayed at the BC twice - the room had serious problems. The first room had two DOUBLE beds, not queen. I am tall, and was VERY not happy. Plus it was tiny - so they finally moved us. To another room with DOUBLE beds. They couldn't move us again until the following day (they said they were full, but now I think I should have refused to let them do that). The housekeeping wasn't good either. In fact, they gave us a free dinner at the Yachtsman steakhouse as an apology, and a free night. The free night we used the following year - my DH had a convention at the Hilton, so we stayed at the BC the first night, then SOG. Well, the free night didn't impress us either. We had scaffolding covering the window to the outside. We just needed a place to sleep so we didn't care.
I am giving it another try in the villas this summer - not concerned about housekeeping as I'll keep it clean myself for the most part (different when travelling with kids!).
The Swan is very clean and the beds are comfortable. It's a longer walk to Epcot, but I like the walk personally. The pros of the Swan are that they have nice room service (or we do carry out from the sushi bar sometimes) so if you're tired at night you can do that (they even have a kids menu for room service and it's reasonable). Plus movies on demand, which sounds silly, but at night it's nice to chill out with a movie sometimes. Disney doesn't have this. The Swan has a nice pool, although the BC has Stormalong Bay.
We've been to WDW so many times, so we like the Swan a lot, as I don't always need Mickey soaps. I'm going for the BCV one bedroom next trip as it's all 4 of us so I like the washer/dryer and kitchen. Plus we do like Epcot! When I go without DH, I love the Swan. It's perfect for the 3 of us. We need 2 rooms if it's all 4 of us.
The Swan has a laundry room, across the way in the Dolphin. I use it every time we stay there; it's fine and right by the Picabu's so you can have a snack while you wait for the stuff to wash.
I personally vote for the Swan.