I've owned two dollies, an old roadmaster that had a swivel plate and an Acme dolly, no swivel plate. My personal preference is the Acme.
The swivel plate is the big plate that the cars front tires rests on. It has a pivot point in the middle and can rotate 15-20 degrees as you make turns.
The non-swivel plate dolly (Acme) relies on the cars steering to swivel when you turn. So when you tow, the cars steering column needs to remain unlocked.
I think the Acme is more friendly with cars that sit lower to the ground, i.e. the Acme dolly sits lower to the ground and the ramps aren't as steep so you won't damage the cars bumper, air dam or skirts when loading/unloading .
The Roadmaster has steeper ramps and can catch bumpers, etc when loading/unloading
DRIVING UP THE RAMPS
The Roadmaster the entire dolly tilts and the ramps were built in and are steeper.
The Acme has long removable ramps, the Acme also sits lower to the ground so I don't think you would ever catch the bumper on your car when loading /unloading.
The Acme ramps are removable, so its a small additional step when loading / unloading. We store the ramps in the trunk of the toad.
You can get brakes on any of the dollys. My Acme comes with a surge brake, I would recommend a surge brake, regardless of the dolly you choose.
ONE PERSON LOADING
Loading the ACme dolly solo is easy. I painted two orange strips on my dolly on the drivers side that shows me where the drivers side tire needs to be to center the car on the dolly. One strip is for the Camry, and the other is for the Civic.
When loading, I install the ramps,
I then roll the drivers window down and I can look out and see the drivers tire.
With my Camry, I drive up the ramp with the left tire just on the edge of the ramp (If I got out and looked, I would see the the right side is also on the edge of its ramp) . This will line up perfectly with the orange line I painted on the dolly and the car will be centered.
I drive it all the way up the ramps until I hit the stop plate on the dolly.
I put it in park, and leave the key in ACC position so the steering is unlocked.
I then strap the tires, and install the safety chains.
I plug my lights into the Camry.
I pull the ramps off and place them in the trunk of the car (Wear gloves, the ramps have sharp edges)
2001 Coachmen Mirada (Ford F53 6.8L V10) - Toad 2001 Civic
It won't do MACH 2, but I can get a sandwich and take a pee.