But my point is, compared to the TV series, Chomper is overly sensitive.
No, not really. You have to understand his position.
In the 2nd movie, he's a baby. Really ,what do you expect? He's been in the world for not even a day, and you expect him to already have emotional maturity? I've seen the movie myself and he never once came across as overly sensitive to me; he was pretty typical and normal in terms of emotion.
As for the 5th movie, he never felt overly emotional there either. He's still a young kid, younger than Littlefoot and the others mind you, but he's put into a new awkward position: he's a carnivore and has been hunting (as evidenced by his parents' lack of surprise when he says he ate a longneck), and then his friends show up, who are all leaf-eaters. His parents would want him to eat them, but he wants to remain friends. But it's not easy, and it's made harder with Cera's distrust towards him now that he's older and more of a threat.
How would you feel if you were put into his position? Imagine if everyone turned on you because you were something they hated, but you couldn't do anything about it.
Yet despite this, Chomper never seems to overdo the emotions. They're kept well under control and he never gets really emo about it. You could say he does in both movies when he walks away crying after feeling rejected, but watch happens later. In LBT2 he's happy again and chasing insects, and in LBT5, he cheers up rather quickly after a talk with Littlefoot and a nuzzle from his mother.