The difference is that Critic works its pop culture gags into the plot instead of just dropping them in at random. Also, most of the time they're actually funny.
Family Guy is basically the Simpsons and the Critic stripped of any wit or timing. It is the product of a man who grew up doing nothing but watching reruns of crappy 80s sitcoms.
Except the Critic was funny and didn't continually rely on trying to be "offensive" or vulgar as it's crutch. Watching it now, yeah, it seems like maybe there were a few too many pop culture gags, but the gags worked, good or bad.
I think this was much funnier, as it had clips that made me laugh. Actually, just one clip that makes me laugh is enough to separate it from Family Guy.
From what I vaguely remember, Lovitz smacked Andy Dick's head into the bar because Dick threatened to "put the 'curse of Phil Hartman' on him". Seriously.