For location and transportation (bus, boat, monorail, walking), the Polynesian wins hands down. You're just so close to everything, which gives you more flexibility. The only negative for me is multiple buildings vs. everything under one roof. (that's why it's my second favorite resort...Wilderness Lodge is my Number One)
The only reason we don't stay at AKL more is because of only having buses for transportation. Otherwise, it's a great resort - beautiful (stunning really), peaceful, great dining options, lots of things to do, and of course - animals. Everything is under one roof here, and if you want to go between Jambo House and Kidani, there is a shuttle. You can also walk, but the shuttle is frequent and easy.
Pro and Con the priorities for your family - You can't really go wrong with either resort, it will just be preference and priority based.
Good luck deciding and have an amazing trip!!