Never stayed at BC, so I can only offer my experiences at BW and what is available there. Whether you have a BW view or a standard or pool, the building is the same, and right on the boardwalk, whereas the BCV is a building outside of the resort, behind it if you will, from the pool area/beach, lake, etc.
We have spent time at the BC pool before pool hopping there was not allowed, my kids liked it, but I didn't like the fact that it was hard to keep an eye on them if they went along the "river", which of course they did! So I was either in the pool with them or trying to work my way around the pool along side it. It is a pretty awesome pool though!
BC has the beach with the movies, as previously posted. I do believe all resorts have some sort of "kids" club. BW has community hall with activities and games for kids, plus the arcade, just off the pool area. You didn't mention the ages of your children, but we joined when our kids were 10. They LOVED the slide at BW (200 foot winding water slide into the pool, like a coaster) at that age, and they love it still at 19. There is also an area for little ones with a water fountain play area. There is a craft time where the kids can join staff members for a daily craft, but I don't know what time that is, you'd have to check with the resort. There's alot of nighttime "strolling" entertainment on the BW - magicians, jugglers, piano players, etc. and the kids love it! There's a face painting booth, and a hair wrapping booth and a couple of carnival games (all for a nice cost of course), as well as a pizza window, funnel cakes, coffee stand, corn dogs, etc. There are a few restaurants, a sweet shoppe/ice cream parlor, and an ESPN sports bar with an arcade. There's also the surrey bike rentals on the boardwalk, and at community hall there are regular bikes for rent. So, between the pool, community hall, and the evening entertainment there's alot going on there for kids and families. Even a few things for the adults as well....Jellyrolls Dueling Piano Bar, Big River Grille & Brewing Works brewing their own beer), Flying Fish Cafe - a signature dining restaurant, etc.
It's a tough choice, both offer alot. Have fun planning and enjoy your trip.