I've stayed at the Polynesian many times and have walked the grounds a couple times at Grand Floridian (GF). The Poly is more inviting and relaxed feeling. Perhaps I'm partial to the tropical atmosphere, but it feels like a vacation getaway. The sounds of the tropical plants when it's raining create a nice atmosphere. Plus you can also walk to the Transportation and Ticket Center, so easy access to the monorail to EPCOT. Really, I think the Poly is my favorite place to stay there (though, we now stay at Fort Wilderness, which during Christmas time is set up great, probably the best place at Christmas due to the ski lodge feel to it).
GF is very sterile feeling when walking around. It's like they're trying too hard to be grown up. Yes, it is very nice, but I feel like I should be all fancy dressed when I'm there. And they have an entire store for designer/fancy soaps, which too me says fancy shopping mall, not WDW. I enjoy a relaxed atmosphere, which is what the Poly provides, plus I prefer the places, both sit down and counter service, to eat at the Poly.
Word of the wise: if you stay at the Poly, even if you are not on ground level you may still not have a balcony, so be sure to request a room with a balcony if you don't want to be on the ground floor. I don't believe there is a price difference, so paying the same price I figure a balcony is a must have (plus I enjoy sitting out on the balcony as it rains).
(Note, if you check out my profile where my profile pic is larger you'll see it is from a room we stayed at a few years ago while it was raining, and the building in the background is the main building for the Poly. IMO that view is one of many great views at the Poly.)