Softbox vs octa vs beauty dish...any difference?

Besides the catchlight shapes they offer, is there any real difference in how the light that comes out of these 3 modifiers in identical sizes affects the subject? I can't seem to spot any...

There are differences between soft boxes and beauty dishes. Even if the same size, the soft box is designed for hotter middle and gradual fall off to create the wrapping light. Beauty dish is designed for smoother light without a hot center and more rapid fall off. An octa is just a round soft box.

HERE is a review I did of different beauty dish type modifiers.

Your question suggests it may be time for a comparison of similar sized soft box, octal and beauty dish.