I think the Simpsons struck first, mocking the family guy for being a rip-off of their show, among other things ... and then Family Guy started to respond. From what I've gleamed, though, it's more good natured ribbing, where-as the Family Guy & South Park writers & producers have actual disdain for each other's show.
I haven't seen much of Family Guy this season. Have they responded to South Park taking a shot at them.