Every time that I've gone down, I've been able to have my choice of cars, and I've done it maybe 8 times or so. Every time I had either an Intrepid class car or minivan.
We had one bad experience on our last april trip - when we got there, there were 3 or 4 cars on the aisle, one marked resvered, and the others were all locked with no keys. The attendant told us "go the the aisle you reserved and take a car from there". So here we were trying to cram our luggage into the car and new cars started appearing on the aisle. There were like 4 other families waiting for EA cars too. I saw a van drive up and told him to not even turn off the iginition, we'd load it right up - which we did. I dunno if it was all of us complaining or just luck, but it seemed like they listened when there were no cars. As we got in line to check out our van, there must have been already 4-5 vans and 3 or so SUV's that were brought in the intervening 5 mins or so. Moral? It may pay to wait a little bit to see if more cars come. it was no more than 10 mins from when I asked to when the cars started appearing. Frustating 10 mins, but they got there.
I also had a problem checking in - when they finalized the transaction, they charged it to my company card on file instead of my personal card. oops! I had to spend 25 mins inside straightening it out also. ugh!
BTW, EA is Free with Disney Club membership - another perk!