If you ever pulled a wagon as a kid, you remember how the front wheels pivoted when you turned. When you use a tow dolly, the dollys wheels are like the front wheels of that wagon, and they need to turn, so the dolly has to have some kind of pivot point, just like the wagon.
If the tow dolly has a swivel plate, the swivel plate acts as that pivot point.
If the dolly doesn't have a swivel plate (Acme EZtow) the cars front wheels act as the pivot point. This is why the cars steering needs to be unlocked when on a Acme dolly.
The swivel plate dolly are a little more convenient to load/unload, because you don't need to mess with ramps, as they are usually built into the dolly, and the entire dolly tilts to lower the ramps.
The Acme dolly has removable ramps. Having the ramps removable allows you more clearance on the dolly, and the ramps won't drag the ground and won't hit the rocker panels on the car.
NOTE - There are reports of the Acme ramps popping off while loading/unloading the dolly. I installed a latch pin on each ramp to prevent this from happening.
Acme EZE-TOW dolly ramps pop off while loading / unloading | 2001 Coachmen Mirada 300QB
Also, the Acme dolly can be stored standing on its end, because there are no ramps.
Someone mentioned the wheel fender clearance. Swivel plates have a very close clearance between the dolly fenders and the car, dolly fenders could hit a wide car or a car not loaded in the center.
The Acme dolly has smaller wheels, and its almost impossible to get the dolly fenders to hit the car.
Both dolly behave the same, If you exceed the turning radius of the dolly, you will drag the dollys front tires sideways in the turn.
Yes, its possible, and with a lot of practice, you could back up either dolly any distance you want. But for the casual, "overshoot the gas pump by a couple feet" . Not a problem, just keep a close eye on it
With the swivel plate, you need to be extremely careful backing, as the dolly wants to go one way, and the car the other. But again, a couple feet is usually not a problem.
Acme - The acme dolly is a lot more forgiving while backing and I can back it much farther (straight line), before the dolly wants to go in a different direction than the car.
Most of the dollys I've seen come with optional brakes. Yes, for the small additional price, get the brakes.
I prefer the surge brakes as they take care of themselves. no adjustments, no connections. etc.
The only item about surge brakes,, you can't back up to far or uphill without installing the locking pin in the surge brake (this keeps it from activating while backing up)