I have stayed at both the Poly and the GF and while I like both of them, I prefer the Poly. Unlike many people, I did not find the GF to be stuffy, but it is more orderly than the Poly with its well-manicured grounds and white trim buildings. The Poly's landscaping is gorgeous, very lush and tropical looking and perhaps a bit on the wild side.
Both resorts have two pools. One big plus to the Poly's volcano pool is that the Castle is centered directly in front of it across the Lagoon. You can sit in the pool at night and watch the Castle change color. Overall the Poly's MK views are better than the MK views at the GF. The Poly also has a much longer stretch of beach than the GF.
The GF has more and better dining options than the Poly and the shopping at the GF is more extensive than the Poly. Remember, however, that the GF is only one Monorail stop from the Poly and one can also walk between the two resorts. Anyone can enjoy the restaurants and shops at the GF regardless of where they stay.
At night there is a band that plays in the GF lobby. At the Poly, tiki torches illuminate the resort grounds.
Regarding transportation, I give the edge to the Poly. It serves the MK via Monorail and boat and the TTC with its Monorails to Epcot is a five minute walk away.
Overall, I find the Poly more relaxing than the GF. It feels magical and like a true vacation resort. In fact, it's my favorite place to stay in the entire world (as in planet earth, not WDW).