Oh, boy, that's a tuff one! And shannonstar, good luck with that split stay idea-I did a split stay between the two once, and decided in the future to do....2 more split stays! It's a great combination-do AK and MK while you're at AKL, then Epcot and DHS from BC.
However, if I really had to do just one, and had the family make-up as the OP, I'd recommend BC. I love Cape May's Character Breakfast, Stormalong bay (including the sandy beach area for the little one and Mom, and if you like ice cream, Beaches and Cream can't be beat. AKL's Mara has some more unique offerings, hummus and pita chips, and there's Sanaa-both might appeal to a more "adult" palate, but I'd lean towards BC for the kids.