You have 5 people. BC will be very packed with a rollaway bed or daybed. AofA will have much more room (you can have a room to yourself!), and the rooms are very themed for kids if the kids like the theme. The pool is also very themed with lots of statues, though no slides. The food court is much bigger with many more choices than BC food court, which has almost nothing, and even more choices at Pop's food court next door, though no sit down restaurants.
BC has a superior pool for the kids, though I find the pool very crowded. BC is also close to Epcot and HS. BC is also fancier, though not near as themed. BC has more nearby restaurants, but if you get there after the gondola opens, then AofA is connected to the same restaurants conveniently if you don't mind gondolas.
Have you tried showing your kids pictures of both hotels and get their input?
If it was me in your shoes, I would choose AofA because I feel that your kids will enjoy the heavy theming there better than they would BC, which is deluxe but not much theming. But only slightly. BC's pool is a huge draw for kids. And you may prefer the luxury feel of BC. So really, either choice will be great. You can't go wrong here.