The Simpsons is better, It's much more universal, I know a lot of people who are in touch with the references used in the Simpsons compared to Family Guy which uses a lot of jokes that focus heavily on American media or celebrity's that Me (being British) and a lot of others don't understand. Family Guy also make unnessacary and poor humoured jokes that sometimes make no sense (even when they don't reference anything which is different to say another adult comedy such as South Park. Another thing I really don't like about Family Guy is the fact that so many irritating kids watch it and constantly quote, one quote I think many of you will be familiar with is when Peter Griffin begins to sing "Bird Is The Word" if your reading this and do quote it, please go and die. Characters is another thing that needs mentioning, Simpsons have very all round characters, you can find a character that you can relate to in the simpsons, however in Family Guy I think it goes a bit deeper, they don't make the character for people to relate with which I like, the use the spontanous qualitys of the characters to make it a lot more funny and expand the character which i don't think many other cartoon comedys do, for example if someone had to describe marges personality compared to Lois Griffins it's easier to do it for marge. However The Simpsons firmly holds as the better show because it hits the goals of both shows which is simply to be a comedy everyone (adults more) can laugh at.
Family guy just uses crude humor to appeal to the lowest common denominator, hellooooo down there Britney Spears! The Simpson's uses real world situations, lazy dad, overprotective mom, juvenile delinquent son, overachieving sister. And the humor is a little more sophisticated and not all about sex and violence.