I've done both a Dollar and a Budget rental in the past couple of years at MCO. I'm not sure if any of the procedures have changed, but here's my experience:
At Dollar, I signed up for Dollar Express and filled out whatever info they wanted. When I arrived at MCO, I was able to bypass the counter in the terminal and go straight to the garage. There was a small counter/booth in the garage that had a board with names and car assignments (a parking spot number). You just go to the car and go. If you don't like the car they assigned, there is someone in the booth that can make a change.
With Budget, I signed up for FastBreak, again so I could bypass the counter in the terminal. Instead, you go straight out to the garage and there is a FastBreak counter there. You wait in line there, but when I went there was only one person in front of me, whereas there were lots of people at the counter in the terminal. They may give you a couple options as to which car you want in the class you reserved. I have heard some people say they are pressured to get additional options with Budget, but my experience was they only asked about the gas and SunPass options. Oh, and if you decline the SunPass, be very careful to make sure it is switched all the way off and I also took it down and stored it in the console of the car. Just make sure to put it back before you return the car. If you have a northeast EZPass, the adhesive system is identical...velcro-like tape.
As far as the cars go, the vehicles I got from Dollar and Budget were fine. I still prefer Alamo due to the ability to go straight to a car if you do online checkin and to easily choose from several.