Is 3/4" OSB a better soundproofing material than 5/8" drywall?
3/4” OSB board is better than 5/8” gypsum board. 

Sound control is measured in STC ratings (sound transmission coefficient).

Here’s a website that tests various materials:  https://www.ecopacificinsulators.com/uploads/4/7/1/6/4716609/sound_transmission_stc_rating.pdf

Gypsum board is not as good as OSB board. 1/2” OSB board equals 5/8” gypsum board. 

As you can see, 3/4” OSB board is not listed, but OSB board increases by +1 for each 1/8” thickness. Therefore, you could surmise that 3/4” OSB board would be +6, and 5/8” gypsum board is +4 and fire rated gypsum board is only +5.