IMHO they kept Schulz doing Peanuts long after he should have retired. I remember in the 90's looking at the current comic strips and thinking, "Why is this so popular? It's not really that funny." But then I found some books of Peanuts cartoons my Mom had from the 70's (or maybe 60's), and they were positively hilarious.
Bill Watterson made the right decision by retiring from Calvin and Hobbes at the peak of his game.
It could be a generational thing as well. I never really "got" Peanuts either, even when reading the older material. Some strips would elicit a mild chuckle, but rarely more than that.
The Far Side on the other hand was always something I loved. I read it in reprints religiously as a kid and collected a number of the books.
it sort of depends on the types of comic you're interested in, but a lot of 'paper comics' have a goal sort of similar to SNL; touch upon the topic du jour in pithy ways to keep your core readership and publisher happy, and lightly enough so as to avoid scaring away potential new readers.
but for a real hurried and simplified explanation : a lot of them exist to parrot a talking point that has been pre-approved by their publisher and coincides with the group think surrounding the publisher and their affiliates.
For me, the appeal of Peanuts was never about amusement; it was about the (simplified for kids) philosophies of life. Even as a kid I could appreciate that Peanuts was a very insightful comic strip, and I'm glad I came across it when I did.
The only thing worse was Doonesbury.