As a brief summary, a PC is a dual action random orbit machine. The head oscillates in a random orbit, and the spinning motion is as a result of this - i.e. the head does not spin as a direct result of being driven around. This means that it spreads it 'energy', making it safer for inexperienced users. If you turn it up to maximum speed, put it on a panel and lean on it, the head will stop spinning. You CAN still do damage and burn paint, but you'd have to be a numpty to do so.
However, the PC can struggle to break down hard abrasives meaning that ultimate cutting ability is compromised, and the ability to break down heavier polishes is also reduced. In reality this means you might need to go over each panel again with a fine finishing polish to remove any marring or holograms that have come about because the PC couldn't fully break the polish down. With enough practice, this can be mostly overcome.
A rotary machine spins the head in one way - it rotates. This means the energy is a lot more concentrated, allowing more correction to be achieved, slightly faster. You can pick up a cheapo Silverline rotary for around £40 on fleabay, but the decent ones are upwards of £150. For a hobby detailer, the Silverline will probably do just fine. The motor has a lot more torque than the PC and it will break down heavier polishes a lot more thoroughly, once you know what you're doing with it. It is a lot less user friendly than the PC, being harder to control and a lot less forgiving - it will go through paint very quickly in the wrong circumstances.
Do a search and you'll get the same thing discussed over and over. There is a 240v version of the PC coming, called the Ultimate Detailing Machine (UDM), its had a rather delayed launch due to one thing and another. It will remove the need for a 110v transformer, and I'm led to believe it will be priced around the £100 mark, so its another option.