I've never liked Family Guy as much as my friends have, nor as much as people expect me to. I could never put my finger on it until I saw the South Park double-episode where Kyle and Cartman are battling to try to save/destroy Family Guy over a 'depicting Mohammed' controversy (i.e. the one that South Park was simultaneously facing for wanting to show Family Guy showing Mohammed in that series of episodes).
South just nailed exactly what annoys me with Family Guy. The Family Guy writing staff as manatees picking random word-balls out of the tank was an awesome metaphor (although that part of its style doesn't bother me that much - it was just dead on as a description), but the part that really nailed it was all of Cartman's comments to Kyle: 'Yes, Kyle, FEEL the anger. That's emotional reaction to events happening the plot! It's a rational response based on characters and relationships constructed during the show!'
I just don't enjoy a series of disconnected jokes as much as humour that's derived from characters and their relationships. In Family Guy the characters' motivations are whatever is needed to get them to carry out the joke. For me, the big comparison point for Family Guy isn't the other cartoons, but the old UK series The Young Ones (the show that started the TV careers of Ben Elton, Alexei Sayle, Rick Mayall, Adrian Edmonson, Dawn French, Hale+Pace...) in that they both do the kind of anarchic sketch-humour of Monty Python and The Goon Show, but within the format of a sitcom with fixed characters and setting. For me, Family Guy just doesn't combine those styles like the Young Ones did - I never got a feeling watching the Young Ones that the characters are puppets for whatever personality/motivation is needed for that episode's joke, whereas in The Family Guy I get that constantly.
And then add to that that Futurama can throw in the occasional moment of genuine pathos (Jurassic Bark, the ending of the Harlem Globetrotters episode, Luck of the Fryrish...), and it makes you realise just how much more weight there is to the characters in Futurama. Family Guy might - in its strongest moments - be as funny, but it can never, ever, move me.
Edit: the other thing that gets me, is that I find the sexism in Family Guy just a little...too...well it's hard to put a finger on it. I've got no problem with South Park, and that's a hell of a lot cruder than Family Guy, and I've got no problems with that kind of humour. It isn't offensiveness per se. It's just...ok you know how sometimes you'll have a group of friends and you'll make bad taste jokes to each other. The jokes can get pretty horribly homophobic or racist, but it doesn't bother you too much because you know that none of you actually 'think' that way (for context, I'm bi, so I'm kind of referring to my own reactions here). You know that you're really pulling the piss out of people who hold those kind of attitudes. Then someone else joins in, and his jokes aren't any more offensive than the previous ones, but...there's just something that makes you uneasy. You just start getting the feeling that this guy actually has a problem with gays or immigrants. The jokes aren't any worse, but there's just something stylistically that seems to indicate a nastier intent behind it - just a little more venom in the wrong places.
That's how Family Guy strikes me with some of the sexist stuff in there. It wasn't like that in its initial run - it didn't go that way until it came back after being off the air for 3 years (between seasons 2 and 3). And, to emphasise my point, seasons 1 and 2 had the most non-pc jokingly sexist content in there. But it wasn't as bothersome - I mean, you had the episode where Peter goes to a feminist retreat after getting done for sexual harassment/assault (groping a co-workers' breasts and saying 'honk honk') and it only gets worse from there...but it's all so absurdly over the top that it isn't offensive. The later stuff isn't as anti-PC, but it just seems to come in in ways that the writers don't seem to be fully in control of. There's just something about the sheer frequency of it that gets disturbing. A few jokes like that are funny in themselves, but when it becomes so bizarrely constant it starts to make me wonder whether Seth really has some kind of obsession with hating feminism. Probably not his intention, but it's just too constant - I mean, they've burnt the joke out seasons ago, and it just gets to the point where I think 'why are you CONSTANTLY running up this flagpole'.
It isn't that any of the jokes by themselves are problematic - obviously it's a light show and isn't supposed to be taken seriously. But there's a difference between the guy who makes one gay joke (assuming it's not an overtly venomous joke) and the guy who is constantly joking about gays every single conversation he has, every time you see him....eventually you start thinking there's a serious problem underlying his 'humour'. I just get that sensation and it kills that part of the show for me.