Well undoubtably, all shows have a finite lifespan, which the Simpsons have certainly out-lived, hence why fans call it "zombie Simpsons". But writing quality has definitely deteriorated. The show became increasingly dependent on guest cameos (something former writers have even noted), premises have been recycled, and there has been much less focus on character development. It's rather hard to imagine some of the old episodes even working in the current show's "universe".
I would argue that most people detracting the Simpsons now, watched it in its prime (Season 2-8).
With Family Guy, the problems are less clear, but one obvious issue is the fact that the characterization of the characters have changed fundamentally since the first two seasons (pre-cancellation). The over-reliance of "sociopathic comedy" would be the biggest problem. The writing also just isn't up to snuff.