We've had AP for a while now. We've stayed on an AP discount a lot of times. Never had any problems with getting a room with an AP discount either. They seem to be very plentiful lately.
On avg, I've found the AP discount to be about 5 or 10% more than the GP discount, just to give you a ball park figure to guess at the nightly rate.
I've even found that we can find an AP room even when the GP rooms are gone, which we did at BoardwalkInn last Friday night.
We've stayed in just about every resort on property since getting our AP (except for the Villas) and have not one time had to show our AP upon check in, even the first time when I booked with just a voucher, hadn't activated the AP yet.