Both Bill O'Reilly and Jon Stewart strive to be on the audience's good side by making jokes and eliciting laughs, thereby relating to their audience and persuading them to agree with their views on these issues. Both sides prove in their statements that they have done their research.
Although Bill's opening statement focused more on government spending (money) and the lack of work among the American people, he explained the concepts in a way that is easy to understand.
Jon's opening statement mainly consisted of not "problems that we have faced before, but we face a problem in our problem-solving mechanisms." and also yes, a lot of what he said with a certain mountain is, of course, mocking. But he does understand that there is a problem between freedom and socialism, a "societal cataclysm". I do believe Jon got his point across a lot more clearly