I would personally go with the regular Beach Club room. The only resorts where I think the studios can really compete with the resort side rooms (and have me consider giving up a bed for a similar cost) are the Grand Floridian and Polynesian. Both those studios are newer than their resort counterparts and themed beautifully. They also have additional bathroom space which BC does not.
The only real benefits a BC studio would have over a regular room is a microwave and a chat set. As previous people have posted, you can use the microwave in the marketplace and the regular BC room has a desk which can be used to eat on. To be honest, BC QS is very limited and unless you want grab and go, salads, or a cold sandwich, you will probably eat elsewhere. There are also tables and chairs outside, in the solarium, and even in front of Beaches & Cream. If you plan on using the pool, you will probably dine at Hurricane Hanna's instead.
I remember your plans are to come from Polynesian. I feel you would regret going from a resort you already like with one of the largest rooms on property with two queens beds to a studio with a sleeper sofa for 2 children. BC really has a lot of wonderful stuff to offer and if you're in a room that you dislike or is lesser than your previous, I think it would negatively affect your overall impression of the entire resort.