I would say you are in a good pickle
They are both fantastic resorts and you can't really go wrong choosing either. I agree with the previous post about staying close to MK at BLT, but there are a few other factors to consider. The travel time to MK from AKL will be between 45 and 60 mins both ways, so if your children do not tolerate long bus rides your may find this to be a glaring negative. From BLT you can easily walk to the park or hop onto the monorail if you would rather save your feet which would only take 15 mins.
Another thing to factor into your decision is what amenities you will be using at the resort. The pools at AKV and AKL Jumbo is fantastic and lushly landscaped, so if you plan to spend a lot of your time poolside I would take that into account. Another awesome feature of the AKL is the proximity to the animals! There is nothing like waking up to see a giraffe having breakfast right outside your window.
BLT can also be spectacular when you wake up and see the MK right outside your window. Your children will be so excited every morning and ready to get to the park! BLT also has a few amenities AKV does not have: access to water sports and a direct boat to Fort Wilderness and WL. BLT is also on the monorail line with connects you to Poly and GF both of which have fantastic dining options.
Dining at the AKV is also a bit of an adventure in itself. Boma, Jiko, and Sanaa serve up some of the best African cuisine, but if your clan is full of picky eaters you will find yourselves eating in the parks or at other resorts most of the time.
Each resort is wonderful, choosing between the two is just a matter of what you are trying to accomplish on your trip!