We've stayed at the GF 7 times and the Polynesian 31 I think. I love them both. Mousekeeping is usually excellent at both.
The monorail makes but a soft whoosh sound wherever you are.

With doors shut, you can't hear it at all.
The rooms at the Polynesian are either slightly bigger in the original buildings or over 50 ft larger in the newer buildings.
More options for transportation at the Polynesian as you can walk to the TTC and take the ferry to MK or the Epcot monorail. At the GF, you must make the whole resort monorail loop and transfer to the Epcot monorail. It is also convenient when returning to the resort to take whichever bus comes first...Polynesian or TTC (MK). You can also do that for the GF but then would need to catch the resort monorail to the GF or make the longer walk.
At the GF, turndown is supposed to be automatic in all rooms and these days it is only automatic in club level at the Polynesian. However, when we were staying in the Royal Palm Club at the GF it took a couple calls to get turndown which was important as we needed the daybed made up. There are also two robes for use while at the GF. Probably my favorite difference at the GF is the hamper for used towels.
GF has two sinks in a dressing area outside the bathroom while at the Polynesian there are 1 or 2 sinks in the bathroom itself.
Decor is very different and I enjoy both.
We too visit restaurants at both and find it fun to "commute" via monorail, small launch or by just making the lovely walk along Seven Seas Lagoon.
Beach situation is better at the Polynesian as there are three and every longhouse is quite close to one of them. Pools are comparable but my grown sons still miss the old slide at the Polynesian!
The grounds of the Polynesian give it a more relaxed atmosphere IMO compared to the more formal grounds of the GF but both are lovely.
I don't think you can go wrong with either.
