Depends on so many factors! We've stayed at both BC (many times) and AKL. BC is our favorite resort based on the factors that are most important to us.
Transportation: We don't bring a car to WDW and love to walk. At BC, we can walk to two parks and take the bus to MK. (Everyone has to bus to AK, so that's a wash for us.) This is a huge factor for us - we make lots of ADRs in Epcot and love to just stroll out the International Gateway and back to our room after dinner. But other guests have other plans or don't mind the bus or drive, so it depends how important this factor is to you.
Resort Area: At BC, we have all of the Epcot resort area dining and shopping within walking distance. We enjoyed the grounds at AKL, but you can only walk so far because it's self-contained. The atmosphere around BC seems more vibrant and the atmosphere around AKL seems more quiet - so it depends on what you'd like.
Theme: I love the beach and I'm not so much a fan of animals. I still really liked AKL, but prefer the pool view! As you can see from photos, the lobbies and grounds are so different - both great, but hard to compare.
Dining: We make lots of ADRs for TS restaurants and prefer a resort without a food court or "food-court-like" location. (If I had to choose a favorite resort CS, it would be Captain Cook's at Poly.) So I know I'm in the minority, but I love BC Marketplace and didn't love the Mara. (Jiko and Sanaa, on the other hand, are two of my favorite restaurants at WDW!) So when people express concerns regarding counter service in the Epcot resort area, that really doesn't apply to us. I did a photo thread a while back regarding the options in the Epcot resort area for CS, and we're quite happy with the options:
http://www.disboards.com/showthread.php?t=2790281
Pool: I love SAB, but the pools at AKL (and Kidani, because you can use that one, too!) are a very close second place for me. SAB is separated into several different areas - some for bigger kids and adults and others for tiny kids. The sand bottom of the pool is fun and our kids loved digging in the sand when they were younger. There is a big slide at SAB, but also a little slide in a shallow pool near the lake - our kids love that little slide! I also have an SAB photo thread that might be helpful:
http://www.disboards.com/showthread.php?t=2790323
The splash pad/water playground area at Kidani is a ton of fun and I actually prefer the AKL and Kidani slides over the large slide at SAB (which is enclosed.) Both Kidani and AKL pools have zero depth entry, which you'll also find in one area (but not all) of SAB. I also like the variety at AKL - fun to try both pools, and the locker room near Kidani makes it easy to hop over there for the afternoon if you're staying at AKL. (Although I'm not sure if the Kidani/AKL pool-sharing rules have changed since we stayed there last year.)
Rooms: I like the decor of the BC rooms and prefer the bedding (down comforter with runner.) The last time we stayed at AKL, they had the "bedspread" type covers. But I thought the rooms at both BC and AKL were in very good condition.
Balcony: It's true that not all BC rooms have full balcony, but we always request one and we've been fortunate that BC has always been able to grant our request. If the full balcony is really critical to us for a certain trip, we'd book YC - they have all full balconies - or BWI. At AKL, we loved our balcony overlooking the pool - great location and really nice view.
BC is our clear favorite of the two, but I realize that different factors are important to different people, so I hope this helps a bit!