Sathi
Simpsons is far better. The writing is sharp and it stays topical. Seth MacFarlane still thinks fart jokes are funny. Yawn.
The Global Geezer
Family Guy. The humour is a whole different level. It’s not the nicer-nice benign humour you get in a lot of American sitcoms, it’s tangenital, random and near-the-knuckle.
Entropy
CURRENTLY, both are utter garbage and should be watched by no one unless your intention is to torture them for information.
However, in it's first 8-10 seasons, The Simpsons was one of the greatest sitcoms in television history and is widely credited with having changed and innovated the genre. It was a pop culture phenomenon of absolutely epic proportions. If you didn't live through it, I literally cannot convey how big the Simpsons were in the early 90s. I can't think of anything that was that big...maybe the entire Marvel franchise.
But around the 8th seasons the Simpsons lost their three main creative forces as well as several very talented writers. The show immediately became a repetitive catch-phrase spewing tragedy that was little more than a parody of itself. It came to embody all of the clichés the show itself once satirized and moved away from.
Family Guy was never even a fraction of what Simpsons was at it's height. It had a couple good seasons before being cancelled, but was never quite the same after it came back. And even going back and rewatching those seasons, they're littered with bad writing. Most of the jokes are completely incidental to the plot. Characterization is completely ignored.
South Park did an episode criticizing Family Guy wherein the version of Family Guy in their show had a writing staff of trained whales that randomly grabbed nouns as the formation of the jokes. It was spot on. Parker and Stone claim that a couple days after it aired, they received a gift basket from the Simpsons writing staff that simple said "THANK YOU!" because of course being on the same network their ability to go after Family Guy is much more fraught with peril.
nineteenthly
I haven't seen the Simpsons for a very long time but when I did used to watch it and 'Family Guy', there was no competition. The Simpsons was far and away the best. Having said that, my views may be way out of date and the quality of the Simpsons may have declined drastically.
Kid Mohawk
Obviously The Simpsons is the better received between the two, but a great number of people feel it's gone past it's prime. Family Guy tends to be the funnier show these days, but the jokes are crass. All in all, I'd say it's a matter of personal preference.
So my own preference would be the Simpsons because it's given me more memorable laughs and jokes.