Susan,
The
Polynesian was recently (2006) renovated, so it has some nice amenities, like flat screen TVs, etc. But the
Beach Club is no slouch, either. While I would opt to stay at the Polynesian, because I have a 1 and 3 year old, you might find the Beach Club more fun. With a 10 and 7 year old you have the great allure of the nearby Boardwalk, the World Showcase in Epcot, and what I feel is a more attractive set of resort-based activities. Also, your family is more likely to be visiting the Hollywood Studios and Epcot parks than a family that spends most days at the Magic Kingdom, so the boat transportation to both is very appealing.
Of course having Stormalong Bay, the single best pool in all of Walt Disney World, at your doorstep is not something you should overlook either!
I am glad to field any follow-up questions if you have them. Just visit my bio page to ask.
Have a Magical Vacation!