I think one of the factors that contributed to The Simpsons' lowering in quality is Family Guy itself. I enjoy Family Guy, but will never hold it in in my heart as dearly as the older Simpsons, where the characters were invested with genuine pathos, the humour, as mentioned already, was often subtle and not over the top, and the plotlines always had a touch of poignancy. Then Family Guy arrived as a parody of The Simpsons, with the same basic family structure, stripping away the soul, and trying to take the humour to the next level of absurdity. It can be hilarious at times, but their determination to always land a gag leads quite often to misses, which can really fall flat, but for the less-discerning viewer can easily be forgotten admidst all the hits.
Since Family Guy's arrival and boom in popularity, the humour in The Simpsons has taken a shift in that direction as well; the plots are increasingly ridiculous and the jokes completely random, and often just as unfunny. The two issues emerging from this is:
1). The Simpsons has lowered itself to mimicry of the Family Guy formula, effectively leading it to self-parody, which Family Guy proves can still succeed, but unfortunately for the Simpsons not if you're,
2). Being beholden to a family audience. Hence, the buttons that Family Guy can push in its attempts to parody the formula give it an edge to appeal to a specific audience, while Simpsons gets caught trying to moderate its insanity to keep the kiddies involved (and Fox happy). Trouble is, you take the 'crude' out of 'childish crude' humour and well you're left with what a lot of The Simpsons viewing experience is like nowadays.
Now that's not to say The Simpsons isn't completely for kids nowadays. Infact, it's probably more political than it's ever been. But unfortunately, I find their attempts at making such statements far too explicit. Personally, overt expression of political views really makes me cringe (see V for Vendetta). Can't we have fun without having to potentially alienate or insult percentages of the viewership for their beliefs? If there's a political gag to be made, a little subtlety wouldn't go astray.
Anyway, incisive political satire should really be left to South Park these days. No one else can compete.