Well, we've stayed at both multiple times, and I'll break it down this way...
Convenience: BWI wins overall, because while BC has the closest door to Epcot, BWI doesn't share buses, and is closer to DHS.
Rooms: Right now, I think the rooms at BC are nicer because they've been more recently updated, though BWI rooms are very nice, and the vast majority (like >95%) have both daybeds and balconies, which BC only has 50% of.
Common Areas: BC lobby is lively, loud, big and airy. It also smells like heaven. BWI lobby is smaller and quieter. I guess it depends what floats your boat. I will say, BWI seems newer, less worn down (it is in fact about 6 years younger that BC).
Food: Again, it's all in what you're looking for. Flying Fish is one of our top 3 restaurants on property. We could take or leave Big River Grille. We think the pizza window and bakery at BWI are superior to BC Marketplace. Both resorts have great character breakfasts. Better drinking options at BWI with Abracadabar, the bar at Flying Fish, and Belle Vue Lounge. At BC, your only option is Martha's Vineyard which is usually pretty quiet. (Yes, I know there are dining options at YC, but first of all, we're talking BC here, and secondly, nothing food-wise at YC makes me jump up and down. Yachtsman was one of the 2 worst meals on property I've had.)
Pool: Ok, BC wins by a landslide, but the pool at BWI is our second favorite on property. It's nicely themed, I'm crazy about the Dumbo tiles around the edge, the slide is really fun (even if it is a clown), and the water always feels refreshing, despite the fact that you're in FL. We do prefer the quiet pool at BWI though, as it's really pretty, especially at night.
Anything else? I don't think my thoughts lean terribly one way or the other. We've stayed at BC more often, primarily for the pool, which is it's biggest selling point. We're actually slightly bigger fans of YC, well were, then the dog policy came along, and we're now thinking BWI for our honeymoon.