I have stayed concierge level at all three of those resorts and like them for different reasons. In my opinion, the AKL and Polyneisan have the best food offerings. BWI has the best location - our room last week was right above Spoodles and we loved the view of the YC/BC and water.
I find the AKL and Polynesian lounges to be more child-friendly. Not that the BWI isn't, but just with the layout - it seems more adult to me. My kids are now 5 & 9 and sometimes they get too wild and I don't feel comfortable with them in that lounge. I usually go and get the stuff and bring it back to the room. (There are no trays out but if you ask they will bring you one)
The staff at all 3 resorts are excellent.
If you are at the AKL on certain days (tues & thurs?) and on the concierge level you can participate (for a cost) in the sunrise safari at the AK. (I know there is also a sunset one but I don't know anything about it.) We went last June and it was worth every penny!
The Polynesian has the great zero-depth pool for the little ones, plus access to the monorail. (when my oldest was younger I used to ride with him on it at night to put him to sleep)
The AKL has the animals! How great is that to sit on your balcony and watch the giraffes??? DD was 4 during that trip and she and I spent a lot of time out there watching.
The BWI has ferry access to MGM and EPCOT. Actually, the walk to EPCOT is quite nice and we walked more than we rode the ferry. The BWI has things to do at night - the AKL is secluded and if you want night entertainment you have to go looking for it.
Three great resorts - tough choice! But no matter which you choose you will have a good time!
Jill