I can help a little. I haven't stayed at Beach Club, but I've stayed at the Polynesian and the GF.
Polynesian:
LARGE rooms (409 sq. feet)
Excellent location - boat or monorail to MK, walking distance to the TTC (to hop monorail to Epcot)
Beautiful landscaping and a true sense that you are isolated from the rest of the "world."
Recently refurbished rooms
Great dining spots ('Ohana and Kona Cafe are two of my most favorite WDW restaurants).
If you get a lagoon view room you will have an amazing view of Cindy's castle and Seven Seas Lagoon.
Private beach with hammocks for viewing fireworks.
Walking distance to the GF for use of their restaurants and/or health club.
Beach Club:
Rooms are a bit smaller here - 380 sq. feet
Large building and your room can be a hike from the main lobby, restaurants, etc.
Great pool - Stormalong Bay
Walking distance to Epcot
In the middle of a lot of things to do (like the boardwalk area)
Transportation is by boat, bus or foot and the boats can take a while. (We've taken boats from here to go to MGM when we were visiting the BW area).
Lots of good dining choices. (Beaches and Cream, Cape May Cafe)
I believe they will be re-habbing The Beach Club soon. I know they're starting on the YC...
To compare these resorts to the GF, I'd have to say that you can't compare the Polynesian to the GF. We were at the GF for our honeymoon in June of 2000 then at the Polynesian for our 1 year anniversary in June 2001. At first I was very excited about the Polynesian. When we got there, though, I was disappointed. However, I was disappointed because I didn't have a lagoon view room AND I was "used to" the light and airy decor of the GF. Looking back now, I really like the Polynesian and I'm trying to convince my DH that when we take our baby (who is still baking

) we should stay at the Polynesian. The room decor is traditional Hawaiin style....bamboo, earth tones.......NOT like the GF which is very victorian. We stayed at the GF again in December and I wasn't as awe-struck by it as I had been on our honeymoon.
Anyway, I don't think that one resort is better than the other......it's just what you're in the mood for with that particular vacation. I would think the BC would be closer in style to the GF and BWI. The Polynesian is definitely in a class by itself.
I hope this helps a little!