But I've watched and enjoyed both shows (though I've watched far more of The Simpsons; I was a fan from the start), and I must chime in with my reasons, and the big one: The Simpsons has a stronger emotional weight. I'm more likely to care about the Simpsons than the Griffins.
That emotional foundation got built very early in The Simpsons's run. The first half-hour Simpsons episode, the Christmas special Simpsons Roasting on an Open Fire, aired December 1989. (The show proper began airing with Bart the Genius in January 1990.) I've long found that Christmas episode actually kind of sappy: it's the one where they rescue the greyhound Santa's Little Helper after he's thrown out by his owner.
(That's one of Bart's relatively rare "wide-eyed little kid" moments, where he's all "Awwww, Dad, can we keep him?" Yes, Bart's a smart-assed troublemaker earlier, like when he blows his dad's cover as a Mall Santa or gets a tattoo, but he's not all about the bad-boy gags. We like him. So we feel for him more later when, say, he gets hit by the car or he's slaving away at that French farm.)
So the whole first episode is motivated by Homer taking desperate steps because he feels otherwise he can't afford a happy family Christmas. (There's actual pathos when he's out in the snow watching other, Griswold-elaborate Christmas displays.) And the show followed that lead, so that at its best (like the Monorail episode), the events of an episode are outlandish, but the emotions aren't.
Family Guy, on the other hand, never built as strong an emotional foundation, and started going outlandish very quickly. That outlandishness can be a thing of beauty -- I adore the insanity of Peter Griffin's fights with the giant chicken, with enormous destruction and death played out to insanely busy Ron Jones action music (I'm a Ron Jones fan) and all of this mayhem having no impact on the plot whatsoever, which is part of the joke -- but it too often feels like outlandishness for the sake of outlandishness. I'm less likely to care.
When Family Guy works, it works (I'm fond of the Griffin kids Chris and Meg, and the music and songs are top-notch; see? More positives!), but I was thinking of highlights and kept coming up with the action stuff: the giant chicken, the knock-down-drag-out battle between Mayor Adam West (yes, that Adam West) and The Noid, or Stewie shrinking himself Fantastic Voyage-style to enter his dad's body and laser-blast his sperm into oblivion. Action is easier to animate than stage, and I admire that Family Guy's writers and animators take advantage of that (especially in, say, the "end of the world" dream episode), but I can't imagine Family Guy doing an episode with emotional action as involved as, say, Homer's vision quest episode (one of my favorites, and the one with Johnny Cash as the voice of the coyote).
And if all that fails to convince you of the greatness of The Simpsons over Family Guy, there's this: Family Guy has never been in a Die Hard film.