despite the coughing, his chest doesn't look "crushed" at all in the movie
Frankly, I accept the portrayal of Grievous in Episode III as the "real Grievous" so I don't need to explain the discrepancies with his behavior in the Clone Wars season 2 finale and season 3 (or the novels or comics for that matter).
His abilities in the cartoon are seriously exaggerated, as are those of the Jedi.
The films are the highest canon and represent the "true reality" of the Star Wars series, so all the rest are interpreted through that lense (at least that's how it is officially).
That said, I enjoyed his portrayal in the Clone Wars cartoon. He seemed a definate threat (though you could tell they were already trying to nerf him in Season 3 to try to prepare for the letdown we'd all see of him in the actual movie this was all hype fodder for), though I thought it was stupid that he had absolutely no force ability. Had he had the Force, I could buy him being so powerful (he was able to leap dozens of feet in the air, and even DODGE the force abilities of Jedi!). But anyway, that's some other character, not the "real Grievous." In my imagination, he had the Force, and he was a mobile droid controller. Now he's just a cyborg general with delusions of grandeur and a few tricks, but that's it.