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.
Vader breathing is a unique and haunting sound. Grevious coughing is a cartoonish and laughable sound. No one cares about explanations, they just want cool and/or scary villains, not absurd cartoon characters.