I agree with ***********, you'll love either one. I think with the ages of the kids though, I would chose Poly. 1) they are going to LOVE the monorail. Just ride the circle, get off at the other two resorts and walk around and explore. It is SO fun to do that! 2) Poly has the zero entry pool that is newly refurbished. The kids will love that too. 3) BI has some fabulous restaurants out on the Boardwalk, but nothing my kids were overly fond of. And walking down that LONG hallway to go outside to get a cup of coffee in the morning, well lets just say I would prefer the POLY set-up for quick bites and such. BI has no type of food court or even a dining option inside the resort itself.
Don't get me wrong, I really liked BI. But you did ask which one and I think for the particular ages of the kids you mentioned, Poly ranks a little higher.