Hi!
We have stayed at both and we LOVE both. In fact, these are our top two WDW resorts.
I'll tell you what I love about each:
The Polynesian:
Location! Room size! Transportation options!
At the Polynesian you will be right in the middle of the magic. You will be able to see the castle from the beach (or your room depending on the category you book), you are a short monorail ride away from the MK and it's one of Walt Disney World's first resorts. Plus they are in the middle of a major room rehab and the rooms are going to LOOK gorgeous!
The size of the rooms are amazing. They're about 409 square feet. You will have two queen beds and a day bed plus a table with two chairs. There is a ton of room to move! We had a crib set up, plus our double stroller open all the time and we still had plenty of room.
You can take the monorail to the MK and you can walk to the TTC to catch a monorail to Epcot, this way you won't have to switch monorails at the TTC like you would if you were leaving from the GF or the Contemporary.
I just love the tropical theming of the Polynesian and the restaurants, Kona Cafe and 'Ohana, are my favorites! It's a kid-friendly resort and it was a big hit with my 3 year old son! We will definitely be going back there.
The Wilderness Lodge:
We love the lodge, too. What I like about WL vs. the Polynesian is that the lodge has all the rooms in one building. At the Polynesian, there are many different longhouses that hold the rooms.
I love the lobby at WL. It is breathtaking! Roaring Fork, the casual food place, is a lot nicer than Captain Cook's, IMHO. There is a larger seating area and it seems to be quicker when you order hot foods from the grill.
The rooms are nice, but not as big. I think the rooms that have one queen and bunk beds might feel bigger, but the rooms are still nice. There are two queen beds, a table and two chairs and all rooms have balconies. There's also a set of built in drawers by the closet which I found to be VERY handy with all the kids items I brought. (Snacks, juice, diapers, etc.)
The boat ride to the MK is great. It is so relaxing and it's nice that you can leave your stroller open. We never had a problem with the buses to the other parks, either. The CM's at WL are SO friendly and helpful! Plus the gift shop at WL sells a lot of things like 1/2 gallons of milk, which was great for us b/c my kids drink a ton of milk. The Polynesian didn't sell anything bigger than a 1/2 pint carton.
So you will not be disappointed with either resort. Both are GREAT and truly embody the idea of themed hotels! We will be at WL in a few weeks and I am getting so excited!
Hope this helps!
Have a magical trip!