Quiet pool at YC is off at the far end of the hotel from SAB. It's on the other side of the hotel from the lagoon, so there is not a lot of activity there. It is a smallish, rectangular pool with room for 20 or so lounge chairs around it. It is set amongst the YC landscaping, so there is some shade and it is very quiet.
The BC quiet pool, meanwhile, is more out in the open. It is not too far off the walkway from YC/BC to Boardwalk/Epcot. Similarly sized pool to YC pool, but not nearly as private. In the evenings especially, there can be a lot of traffic by the pool from people returning to the BC who go by the pool to enter the BC there, rather than going down to the main BC entrance.