I think if your top priority is the speed of getting to the parks, pick BC. This may be especially true if you are trying to cram in alot of rides and attractions. On the other hand, if your top priority is a unique and beautiful resort that transports you to another continent, pick AKL.
The AKL is unique and beautiful. The Travel Channel rates AKL the #1 Family Resort on their World's Best lists. The BC is nice, but looks alot like many other places. I prefer taking the parks at a relaxed pace and spending a good amount of time relaxing at the resort. For that, AKL is my favorite.
Stormalong Bay is SOOOO popular, but it is not for me. As a single parent, I don't like how spread out it is, especially the slide. I don't like going on the slides, so I usually wait at where they let out to watch for my daughter. At Stormalong Bay that meant she had to be out of my sight for a long walk to the slide entrace. This included walking past the Boardwalk area where lots of people walk by who aren't even using the pool or staying at the resort. It made me nervous! I also was disappointed with the hours at Stormalong Bay. When we were there I believe the Stormalong Bay hours were from 10 a.m. - 8 p.m. The AKL pool is open 24 hours. We take advantage of this to enjoy a late night swim or an early morning swim before checkout. BC does have a quiet pool that is open 24 hours, but I thought it was pretty boring. I thought the AKL pool and surroundings were beautiful.