Hi, Patty!
You are choosing between two family favorites! My family loves both of these resorts. The Contemporary has amazing views from its Tower Rooms, and the 4th Floor is so much fun with Chef Mickey's, Contempo Cafe (food court) and great gift shops. Being able to walk to the Magic Kingdom is a real bonus.
However, if I have to choose one, it is going to be the Polynesian. You just cannot beat the tropical theme, the beautiful beach, and fun Volcano Pool. Some our best Disney vacation memories are lounging on the beach in the evenings watching Wishes! at the Magic Kingdom. Toss in the Electric Water Pageant and movies on the beach, and you just cannot beat the Polynesian. While you will have to pay a bit extra for that 3rd adult in your room, the sleeping situation will be comfortable with 2 queen beds plus a daybed.
Both the Polynesian and Contemporary have Quick Service dining options. Captain Cooks at the Polynesian has a
complete menu with flatbreads, burgers, and great stir-fry noodles. Kids can enjoy a grilled cheese or pizza to name a few items. The Contemporary's
Contempo Cafe's menu has flatbreads, sandwiches, and even sushi. Kids can get everything from chicken nuggets to a mahi sandwich.
While the cabins are nice, I think the Polynesian is very convenient to transportation, quick and easy access to the food court, and the awesome monorail to Magic Kingdom and Epcot. If you end up choosing this resort, I hope you enjoy it as much as my family does. Good luck deciding!