Hi Paul,
Welcome to the Moms Panel! Deciding on a resort is one of the biggest decisions when planning your Walt Disney World vacation. I have stayed at both the Polynesian and Animal Kingdom Lodge, and although I really enjoy both resorts my preference would be the Polynesian.
I love the the atmosphere and experience of the Animal Kingdom Lodge, however I dislike the remote location. The only method of transportation available is busses, unless you plan on renting a car.
I found the location of the Polynesian ideal, and the rooms were more spacious than they were at the Animal Kingdom. The swimming pool at the Animal Kingdom is quite a bit larger, but they both boast the zero-entry feature which is great with little ones!
One of the websites I find most helpful when trying to choose a resort is
www.allearsnet.com They have a fantastic library of resort photos that are well organized and detailed. Simply click on their accommodations section to view.
Hope this helps, good luck with your decision!