This isn’t an argument over which is better, just which is more offensive.
Of course they’re both pretty offensive, but despite not being able to do all the stuff South Park can do (see the Scott Tenorman episode), I feel more guilty when I laugh at many of Family Guy’s jokes which feel so, so wrong yet hilarious. Like the Anne Frank joke for example.
I reckon Family Guy packs in more to be offended at per episode than South Park does. South Park seems to go for Offensive Theme of The Week style. Family Guy packs in offensive asides as it barrels along.
Am I offended? No way. 
No question - South Park
Examples
ANTI-SEMETISM
South Park:
Pretty much anything Cartman ever says to Kyle
Best line
Kyle’s Cousin “I’m just having trouble with my concentration”
Cartman “Maybe we should send him to concentration camp?”
Family Guy:
Peter hires a Jewish accountant to fix his financial situation…woo edgie
Best line
Peter “You guys are good at everything…except manual labor”
Lois “Peter, don’t say that…they built the pyramids”
Advatage South Park
THE HANDICAPED
South Park:
The cripple fight between Timmy and Jimmy
Best Line
Timmy " D-D-D-D Down like a clown Charlie B-B-B-B-Brown…"
Family Guy
The wheelchair bound cop neighbor
Best Line
Stewie “Now machine!! DO MY BIDDING!”
Advatage South Park
DRUGS
South Park
The kids parents hire actors to play future versions of the kids on drugs. The kids cover their house with excrement in revenge.
Best Line
Cartman “Screw yew! I do what I want!!”
Future Cartman “Aww CRAP!!! [Turns into fat 30 year old loser]”
Family Guy
Peter attends Megs school as “Lando Griffin” to stop the kids from doing “Toad”.
Best Line
Lando “Now I’m off to drive my motorcycle recklessly up to Dead Mans Curve!”
Advatage South Park
BATHROOM HUMOR
South Park
Stan learns he can crap out his mouth by shoving food up his ass
Family Guy
Brian has trouble peeing on the carpet
Advatage South Park
As I said, no contest
First off, the examples you provided are a mere speck of the full spectrum provided by both shows. Furthmore, everyone you mentioned is higly subjective, but it is your optinion, so…
Anyways, I’m going to have to side with Family Guy. Despite it not having as many swear words, I’ve found it to be far more potentially offensive than South Park. Note that I’m not offended by either show in the last.
Argh, I meant to preview that. Anyways, please disregard the spelling errors.
Southpark is too self-aware to really be offensive. They craft episodes (with great skill, I might add) to justify the outrageous bits. Family Guy has had moments (not a lot, but one or two are enough when Southpark has had zero) where you can tell that the joke was the only thing that mattered to them, and any justification for the offensiveness was after the fact.
Well, personally, I’ve never found either to be offensive.
shrug
It’s too subjective… I find both to be absolutely hilarious. SOuth Park justifies it’s humor by trying to have a “Jerry SPringer Monologue” moment at the end of each show, usually by Kyle… (again this is a generalization) - They have more topical, current humor…
Family Guy just throws it out there with no apologies…I think that Family Guy humor is geared more towards “80’s” kids…they make shows based on stuff we grew up with…
For example :
etc…
The thing I love about Family Guy is that they are constantly doing random “asides” during the show that are hilarious…usually 1-3 second flashbacks or fantasies that always crack me up…
Well, I know which one insults me more… Family Guy.
I would venture to say that South Park aims more at a “in your face” approach to it’s off colour humour, while Family Guy uses the throwbacks to use the subtle approach. They both excel at offending people. I won’t tell you why I had a g/f dump me because I laughed at the Pokaru episode of South Park.
I personally prefer Family Guy.
Although that episode didn’t air because of the perceived offensiveness of a stereotypical Jewish accountant, that’s a pretty lame example. How about the “Das Gym” sequence, where it’s implied that Hitler started the Holocaust because he was picked on by a bunch of muscle-bound Jews? Or how about the Holocaust-denying tour guide in Berlin?
How about when Peter first learns Joe can’t walk? “Holy crip, he’s a crapple!” For that matter, how about the episode where Joe enters the Special Olympics knockoff and is bested by the foul-mouthed guy with the Stephen Hawking voicebox? Of course South Park looks better if you don’t even pick good jokes. 
Much funnier in context, when you consider most of the episode is a Grease! spoof (with references to lots of other high school movies like Fast Times at Ridgemont High, The Breakfast Club, Ferris Bueller’s Day Off, etc.) and that Peter gets the kids to swear off drugs by leading them in a song.
None of it offends me personally, but I don’t like South Park. I think offensiveness-as-humor becomes unfunny when you wear it on your sleeve. The SP kids curse so much I get immune to it and it isn’t funny. And when you watch South Park, you KNOW they’re going to do that just about non-stop every episode, so they’re just fulfilling your expectations. (It also makes a big difference that they’re on late-night cable, and Family Guy was on FOX in prime time.) Family Guy surprises you by doing it occasionally and at very random moments, which I much prefer. It’s just more creative.
I don’t know. A lot of times South Park will include offensive things in order to make fun of them, whereas Family Guy includes offensive things because they are funny. Although there’s a lot of crossover, I think this is a big deal. Yeah, Cartman says some pretty offensive things, but he’s an idiot and everyone hates him. And remember in the South Park movie when they had Operation Human Shield and Operation Get Behind the Darkies? IMO this takes more talent to pull off than dropping it in at very random moments, and it’s less offensive too.
Not that I don’t like both shows.
I have to give the edge to South Park, because of the sex education episode. Has Family Guy ever done anything on a par with 9 year old boys sexually stimulating dogs onscreen?
Same here, why would people be offended by cartoons? I mean, it is comedy… I find CSI episodes much more offensive than either one due to their sheer stupidity.
Can’t you find it offensive and funny? That’s how I feel about both of them, although I watch SP more often.
I dunno, I think the “Hennifah Lopez” episode had even that beat, when Cartman…
… gives Ben Affleck a handjob.
I think Family Guy does bizarre humor better, c.f. crazy major Adam West (voiced by 60s Batman Adam West) convinced someone is stealing his water whenever he turns on his faucet. Priceless.
No one has seemed to bring up the more offensive Family Guy stuff, like:
Peter saying his appetite has gotten him in trouble before, then cutting too a black and white WWII scene. Nazis break down a door and enter a house, while in the attic a family hides while a girl holds a diary. Everyone’s quiet and tense until Peter starts to loudly eat potato chips.
A young Peter bursts in on Charles Manson and his family then says, “I’ve been invited to a party at Sharon Tate’s house. You can all come but you have to promise not to embarass me.”
Another Polanski joke where Lois bursts in on Stewie having a kid tied up. Lois is bewildered, but Stewie just replies, “We’re playing house…Roman Polanski’s house.”
And there are more, but you get the general idea.
And I agree dantheman in that they’re both funny and offensive. I don’t see why most people here think those two things are mutually exclusive.
That’s not so much offensive as it is disturbing.
I think Family Guy is less offensive, and a lot funnier - it takes a much, much subtler approach.
Yeah- what exactly IS offensive here? Not to make this too philosophical, but I don’t see what’s so offensive about some of these things here.