Futurama. Not even close.
Family Guy is a lot of toilet humor and it's kind of like South Park now where I think (keywords: I THINK) the creators know that the only reason people watch the show is to see how far they'll push the envelope. Family Guy also uses cheap cutaway gags that are funny once, but can sometimes go on for way to long. The earlier stuff is okay, but a lot of the shows material of the past year or so has been terrible, both in storytelling and in what it brings to the table in humor.
And truthfully, sometimes the jokes feel forced. As if they shove it in just because it's an omg they did not just go there kind of joke.
Futurama has some great humor, and while it pushes limits, it never really gets too dirty. The stories, the characters, and the world are also much more memorable to me. And sometimes, the series can hit nerves. I think one of the saddest episodes of a TV show in general was the episode Jurassic Bark. I dare you to watch that and not have tears in your eyes afterwards. The show has moments that break through the humor and show the characters in different lights.
Futurama has jokes, but also tells stories and offers moments that make you think. It's a show with a lot of small jokes, some which only the smartest people can understand (i'm not one of them sadly), that can sometimes make you think "wow! They put that in there!". Family Guy has some great episodes as well, but the show really gets it's ratings from its dead center jokes.
But to each their own. Family Guy has earned its place and I do enjoy watching it every now and again, but nine times out of ten, if Futurama and Family Guy are on at the same time, I'll be watching Futurama.
EDIT: Thanks to mjc0961 for pointing out my mistake at the end there.