I have stayed at both. A split-stay at BC and WL when DS was 3 and back to YC this past summer (I know, not BC, but same location and amenities). I, personally, would never stay at WL again with a young child. The transportation, entertainment and dining options are far too limited. Everyone keeps mentioning proximity to MK as a pro for WL. It may be close, but you still have to take a bus or a boat and I found the transportation to the other parks to be incredibly slow - when I was there the bus was shared with FW - it took FOREVER to get to DHS and EP.
If you were considering a monorail resort - I would say it is a toss-up. But WL's proximity to parks and dining and entertainment options simply do not compare to what is available to you in the BC area. Especially if you are considering taking your children back to the resort to rest or nap in the afternoon. If you do that at WL, then you are either stuck at WL post-nap with three dining options (AP, WC and a CS) OR you have to get back on a bus, boat or take a cab to get anywhere else.
If you go back to BC to freshen up or nap, you can then simply put the children in their strollers and have a myriad of restaurant and entertainment options just a walk away.
DS and I had so much fun when staying in the EP area - we would walk back into WS post-nap or post-afternoon swim for a walk, dinner and Illuminations. Go over to the Boardwalk to play the games, take a surrey bike ride, have a nice dinner. Explore the Swan/Dolphin, etc.
I vote BC with younger children HANDS DOWN!