Seriously, Vaders breathing didn’t get explained in movies till 20 years after there was 3 movies of him breathing. So what’s the big deal that Grevious coughs? Anyway, that was explained in the first clone wars cartoon. I checked out the dvd and saw it myself. Mace windu crushes his chest with the force.
I’d say seeing Vader without the mask, first only a bit of him in Empire, then completely in Jedi, should be enough explanation for his breathing.
I probably wouldn’t mind Grevious’ coughing, if Vader hadn’t had it before. Two villains with the same kind of breathing problems is simply unoriginal.