yes, his business is ripping on people, most of it (against celebrities anyway) isn't very serious.
I've heard him criticize Leno as being phony and a shell of a man (compared to the comedian he used to be), and it's funny and kind of true, in his interviews on the Tonight Show he's on autopilot and not listening to the answers he's getting. It's as much a rant against all Hollywood phonies as anything. Also, Stuttering John was hired away by the Tonight Show, so that's an opportunity to go off on Leno, and although I quit listening regularly before that happened, I've heard that's exactly what Howard did and probably is still doing.
And if you want to get right down to it, in the case of Leno & Letterman, there's probably some jealousy on Stern's part as he's voiced interest in doing a late night show in the past, but no network will touch him.
Oh and if you've never heard his fake Dave Letterman on the radio, that's hilarious, the guy's bad timing and delivery and failed attempts to crack jokes not on the script are maybe the funniest part.