Both are great resorts, and we've stayed at both multiple times. If you've never stayed at the AKL, just do it. There is nothing like it ANYWHERE else in the world. (Ok, maybe somewhere in Africa...)
Others have pointed out that some rooms have a maximum occupancy. Check with both resorts to see which is a better fit for your situation. I've stayed at the Concierge level at the WL, but IMO it isn't necessarily the best use of my $$$. We are a family of 4, and when we travel with my MIL, we either get adjoining rooms with a lockout, or rooms that are very close. We are expecting twins (yikes), so we will soon be a family of 6, which will mean that we will be over conventional max occupancy going forward.
Others have pointed out that they prefer the WL for it's proximity to MK, but it is also on Bay Lake, which gives you access to the campgrounds, boating (water sprites are a good deal for the kids!), fishing, and access to the other MK resorts (GF, Cont, Poly), which have some of the best restaurants on the property. AKL has Jiko and Boma, which are 2 of my favorites, but not for everyone (there's a lot of sunburnt tourists looking at menus saying "What's this?"- makes me laugh.)
AKL has animals. Everywhere. It is very close to the AK park, which makes it convenient to AKL (5 min) and very secluded(no fireworks). As the least visited park, away from the masses, I think it is much more intimate. Sitting quietly on the balconies as giraffes pass your window is sublime, especially knowing that you didn't need to take malaria pills. The AKL is spectacular, but decidedly "low key". If you need to unwind from life, AKL is the better place to do it.
Steve
WL in two weeks! (chose it for a short trip 5 nights vs normally 8-10 nights because of the transportation/proximity. DS7, DD4+me and the Mrs.)