Ah, I had not seen that one. I knew he told Papa Bear to go f#?k himself at some point, but I did not know why.

I might be completely off on this (especially since Colbert takes everything personal anyway), but I find it interesting that what made him snap was an insult to his professional abilities to host his show, whereas Stephen was only hurt and disappointed as he thought O'Reilly treated him like dirt on a personal level.
My interpretation would be that there are two main layers in Stephen's relationship to O'Reilly: On the one hand (and that's the one the real Stephen seems to agree to to a certain extent) he admires O'Reilly's ability to host his show ("1 hour 5 times a week + the radio factor"), sees him at the same time as a role model and a rival.
On the other hand, he also sees him as a father figure, just wants to be loved and would "do everything he says".
So he would react differently, but as I said, I'm far from sure and it's a very spontaneous theory that might be very off.