tbh you could make a decent case that South Park is the only one of the three that has bothered to try in recent years (or even improved?). It goes without saying that the modern Simpsons is downright embarrassing to watch, like watching a close friend bomb at stand-up before soiling themselves; modern Family Guy is much better, but still unfathomably lazy. the trouble is both these shows have kind of dated premises: the old sentimental and ultra-sanitized family shows of yesteryear have long been buried in a sea of irony and postmodernism. Heck, the most iconic image of The Simpsons - the family all rushing in to watch TV at the same time - is alien to people less than a decade younger than me.
By contrast South Park - although I'm not a regular watcher by any means - does seem to be adapting with the times? It's introduced seasonal arcs, shed some of the mindless contrarianism that defined it in earlier seasons and been intriguingly self-critical.
One thing I've been thinking about recently is how culturally strange if not incomprehensible many early episodes of
The Simpsons must now seem to those who are young now. Especially just how many of the narratives are driven around TV and its culture in a way that now strikes me at least as extremely 90s (as do the Gender stereotypes attached to it).
But then again
The Simpsons is now an old show, the oldest full length (never mind the shorts) episode came out in 1989, so we are as close to it now as the audience in 1989 was to 1959 and, quite frankly, the pop culture of 1989 feels a lot closer to now than the pop culture of 1959 did to that of 1989.