It depends on a lot of things: the size of the hospital, the size of the city, etc.
I've only used Casualty once in the UK and it was a breeze. In and out with really good service and, as others have said, no bill at the end.
I've used the ER a gazillion times in the US (for my mother) and we never waited less than 6 hours. It was usually overnight. And it was sheer hell, and something I hope I never have to go through again.
Having said that, the place I went to in the UK was a small hospital in a rural location. The ER in the US was a large urban hospital in a pretty densely populated part of the country. I wouldn't be surprised if the results were completely opposite if you went to a small quiet rural ER in the States and a big inner-city Casualty in London. Does anyone know?