This is guaranteed to get a discussion going. I own at Boardwalk but I'll be at Beach Club next week. Both are great resorts, have their own styles and you won't go wrong with either.
Pools: Stormalong Bay is the best pool at Disney, but it's hugh. You can easily lose sight of people. It has a great slide and a sand bottom. The lazy river is very nice, but deep and fast moving. Not really a place for an unsupervised child. The Boardwalk pool is very nice, has a great slide (a large clown face) and is smaller. Both resorts have very nice quiet pools.
Restaurants: Beach club may have the edge. It has Cape May Cafe there, with a character breakfast and it also has a place to have a more informal breakfast. Boardwalk has the bakery, a short walk outside and Spoodles does a nice breakfast. Meal choices for dinner are equal, Flying Fish and Spoodles vs Yachtsman Steak house and Cape May.
Location: Both great locations. Boardwalk is closer to MGM and an easy walk from the villa's. It's also a quick walk to Epcot, less than 10 Minutes. Beach Club is closer to Epcot, but not significantly.
I guess what it comes down to is both are great and a easy walk to each other. I like the Boardwalk lobby better, but you don't live in the lobby. I would choose eithor without giving it a second though. Let the availability determine your choice.
One note, the Boardwalk has rooms that overlook the Boardwalk. This can be a selling point. The view is very nice but can be noisy if the doors are left open early in the evening. Noise is not really a problem unless you sleep very very lightly. Boardwalk villas also have standard view rooms which are less expensive.