He is a sack of organs, he never needed any further explanation for the cough.
Also Greivous has tons of intimidating moments in the show.
Watch the Episode "Lair of Greivous" where he kills a Jedi Knight in one of his first appearances on the show.
In "Massacre" he genocides an entire planet, slaughtering legions of Nightsisters.
In "Son of Dathomir" (a comic based on unaired episodes) Greivous goes toe to toe with Darth Maul, and also kills the Nightsister Mother Talzin, who was in a seemingly-even match against Sheev.
Meanwhile Genndy Greivous is basically Greivous in appearance only, ridiculously able to fight and kill multiple Jedi Masters at once. Fun to watch once, but it really doesn't fit Star Wars at all. All style, no substance.