We have three boys (ages 6, 12 and 13.) We've stayed at Poly and BWI with the kids, and in just two days we're headed to WDW to stay at both! We'll start at Poly and spend lots of time at MK and a little at AK. Then we'll transfer to BWI and spend more time at Epcot and DHS. So a split stay is a great way to enjoy the benefits of both resorts.
But if you're trying to choose just one, I'd go with Poly for your family. As previous posters have mentioned, it's so convenient to MK. It also have a zero depth entry pool, which is great with little kids. And then there's the beach and the fun tropical atmosphere. Captain Cook's is our favorite CS in all of WDW and it's really convenient with kids. Also open 24 hours, which is just nice to know even if we don't need it to be open at odd hours.
Good luck with your decision!