Franchesca, the cheap dorm-type reefers don't have the high-efficiency type compressors, and usually won't run off 12V as well as 120V. Most aren't specifically designed to withstand the vibrations of travel, either. The high-dollar compressor types use a much more efficient motor and compressor, and the compressor & gas plumbing are designed more ruggedly.
The big advantages of either type compared to a 3-way are that they cool quicker, and can run off-level. A lot of them used a computer-type muffin fan to improve heat rejection.
Jim, "Mo' coffee!"