First off, never ever ever use a beauty dish on someone that is not beautiful, go with something bigger. Second beauty dishes produce more contrast and zip than boxes do, they have a more specular quality to highlights they produce. Third they have a very different falloff pattern than soft boxes or umbrellas do. Fourth, the good ones that have a glass or plastic translucent center diffuser have a hot spot in the center portion of the light pattern that they throw. In my opinion these are the reasons that you want a beauty dish in the first place, not just because they are sort of big. If it is just the size of light that you are after soft boxes are way easier to carry around especially the smaller ones that are the same size as a dish. If you want just a round catch light a circular mask on your box will do the trick, also easy to carry around. If you want less spill, nylon grids are great on a box.
The reason you want to use a giant pain in the rear dish potentially with a giant pain in the but expensive grid is again more contrast, specularity in the highlights, falloff pattern, center hot spot. If you move the light too far away with a beauty dish you lose the fall off pattern (at least the part you care about), you lose that hotspot because it gets big enough to cover your entire subject and you end up with something that looks not too different than a small regular old reflector. Thatâ€™s why you have probably read about beauty dishes having a â€œsweet spotâ€. That â€œsweet spotâ€ is pretty much pretty darn close to your subject that is placed in such a way that it uses the hot spot and fall off characteristics in a way that is pleasing to the image.
In this image I used a beauty dish, the effects are subtle as always compared to a box of the same size but they are there. The dish was about 3 feet away from the model and there was a white reflector under the modelâ€™s face just out of the frame. If you look close you will see that the face is a bit brighter than the rest of the skin. This is the hot spot. If you take a look at the highlights on the nose, and lips you will see that they are a bit more sparkly than they would be using a box of the same size, this is again due to the hotter, brighter center that the dish has versus a double diffused soft box. Other than that there really isnâ€™t a whole lot of difference between a beauty dish and a soft box of about the same size. Maybe the dish puts out a bit more light as well if you are starved for power. One last little point, if you put diffusion in front of a beauty dish or itâ€™s too far away from your subject the more and more it will look like a soft box. Just way more expensive and way harder to carry around.