Beauty dishes are really gaining in popularity due to the DIY craze, as well as the flood of cheap Chinese-made beauty dishes that are priced at only $59, to $89 with a honeycomb grid and diffuser sock. The beauty dish has a number of things going for it; an odd combination of diffused light due to the shroud, and 'some' hardness to the light, especially at longer distances, since the light is only typically 20 or 22 inches in diameter.
Beauty dishes are also low-profile, not deep, like a traditional softbox, or as long as an umbrella with shaft, so they can be used in garage studio type settings where the ceiling are not very high, and still provide a high, overhead main light or accent light. They often come with a white nylon-faced drawstring diffuser, usually called a diffuser sock. Honeycomb grids of usually 20 or 35 degrees are also available, which further allows you to restrict the light, for more control. Also, the 20 and 22-inch models will usually accept 2-door barndoors AND snap-on diffusers (Speedotron make superb snap-on mylar diffusers and decent barn door sets), so there are honeycomb grids, diffusers, and barn doors available from Speedotron,and other makers, that will also fit on the Chinese-made standard-sized dishes. Due to the design, a beauty dish is actually pretty easily modified or subtly changed, with the diffuser sock, or the grid, or the barn doors, or combinations thereof, being able to be fitted to the light in just seconds.