I have to say that I would go with AK over a moderate. I find that the AKL is a littel more laid back. I like the one bus stop with AKL (sometimes a stop at Kidani) and I like that its not so spread out. And I like to order room service for breakfast a couple times during my trip. A room service tip: order pancakes, one adult and one child, you get plenty to share. This is awesome to do on your checkout day. The kids can eat in their pjs, while you pack. Room service gives you plenty of time to get ready wityout any rush or stress.
I prefer to stay in the villas. I rented points. I save money and get pool view.
Not sure of the ages of your kids, but I find it to be too much to do a Disney trip and other parks at the same time. Its just too much unless you kids are older. Mine are 8 & 11 we did Disney/SeaWorld/and a local stop my mom wanted, a couple years ago. I said never again, I was so worn out.
Enjoy planning, AK is one of our favorite resorts.