I have to agree with Ducklite. We've stayed at both, and as I said before, my son (who is younger than your kids) liked AKL better. DH & I love it. But both resorts are nice for different reasons.
One main disadvantage we found to the Polynesian (as mentioned by ducklite) is that the buildings are not connected. If it's pouring, which often happens, there is no way to get to anywhere without getting drenched. At AKL everything is connected or under an overhang.
The Polynesian rooms are bigger.
The AKL has more to see, we could watch the animals all day. We liked the AKL pool better, but in December you might not get to go anyway.
As far as breaks, the parks are open late during the holidays and you will have enough time to get back to either resort.
One main disadvantage we found to the Polynesian (as mentioned by ducklite) is that the buildings are not connected. If it's pouring, which often happens, there is no way to get to anywhere without getting drenched. At AKL everything is connected or under an overhang.
The Polynesian rooms are bigger.
The AKL has more to see, we could watch the animals all day. We liked the AKL pool better, but in December you might not get to go anyway.
As far as breaks, the parks are open late during the holidays and you will have enough time to get back to either resort.