We have never stayed at the AKL but have stayed at the CBR twice. We loved it both times.
The CBR is very centrally located so it never took long ot reach any Disney destination. I remember timing our ride to MGM Studios and it was just 11 minutes. That was from the time we boarded the bus, made our rounds around the CBR and pulled into the MGM Studios bus stop. The ride to the other parks was short as well. The buses ran very efficiently and we never waited long for a bus to arrive at the bus stop.
At the CBR each village has their own quiet pool and white sandy beach. The beaches have hammocks and beach chairs with some having small playgrounds.
Old Port Royale is where the food court/main pool/marina/store/restaurant
is located. The promenade around the lake is just 1.4 miles so, even if you were in a village at the furthest point, your walk to the OPR is just half of that. If you want, you can pay for a preferred room location and you'll be placed even closer to OPR.
The food court at the CBR has something for everyone. The grab n go station was our favorite. They had fresh made sandwiches, salads, yogurt, fresh fruit, boiled eggs and lots of bakery items. Other stations sell pizza, pasta, salad, burgers, hot dogs, chicken strips (kids' chicken nugget meals come in a sand pail they can keep and play with on the beach), roasted turkey, deli sandwiches, veggies, etc. At breakfast, you can find Mickey waffles (plain or with fruit toppings), assortment of breakfast meats, omelets, etc.
The store at the CBR has a large variety of items to choose from. One side sells pirate and tropical themed items and the other side sells the more traditional Disney merchandise such as t-shirts, hats, toys, etc.
Hope this helps in your decision making process! Lisa