This is a difficult question because these are both great hotels. There are a few factors you should consider in making your decision: which park you will visit most, your children's interest in swimming, where you will be having your evening meals, and the amount of space you need.
If you will be spending all your time in the Magic Kingdom, then the
Polynesian is a great choice. You can roll a stroller on and off the monorail without having to fold it. (Big bonus points in my book.) And you have easy access to the character meals at the Grand Floridian and the Contemporary.
However, if you will be spending any evening time at Epcot, then I might go with the Beach Club. If you're at the
Beach Club Villas, you can finish your dinner in France or England, and with a quick walk back to the hotel, you can be tucked into bed 15 minutes later.
Also, while the Polynesian has a lovely pool, the large pool at the Beach Club is truly spectacular -- a mini-water park of your own with features to entice each of your children.
Finally, the space difference between villas and regular hotel rooms is considerable. With a villa, you get a second bathroom and another room that you can close off while the baby is napping. Also with the villas, there are in-room laundry facilities and a real kitchen. I am very anti-housework when I am on vacation, but those villa features have saved my neck on more than one occasion. As I said, you can't go wrong with either choice.