Part of the humor of Mark Twain's story is the juxtaposition of the two narrators: one of the outer (frame) story and one of the story-in-a-story. The outer frame's narrator, known only as "I," is polite, formal, well-educated, from the East, and perhaps slightly irritable, or at least irritated. In contrast, Simon Wheeler is rather inconsiderate, relaxed, possibly poorly educated, from the West, and good-natured.
The first narrator makes a polite and very formal inquiry after a friend of a friend, telling Simon Wheeler that if he could supply any information, he "would feel under many obligations to him." He displays his formality and education by using fancy ways of conveying simple information, such as saying "a cherished companion of his boyhood" rather than simply "an old friend." The narrator's education and the fact that he has a friend from the East suggest that he, too, is originally from that more civilized part of the country. The narrator speaks of being bored to death and exasperated, showing that he is somewhat irritable or that he is irritated by the fact that he has been the butt of a joke by his friend. He seems to take his leave in the middle of Simon Wheeler's sentence. To be fair, the narrator is probably feigning his irritation; nevertheless, it stands in contrast to Wheeler's disposition.
Simon Wheeler is quite different. Although he is certainly friendly, he lacks proper manners in that he infringes on the narrator's personal space, backing him into a corner and blockading him there and speaking non-stop. While the first narrator is stilted in his language, Simon Wheeler is unrefined and informal, using idioms, contractions, and colloquialisms freely. For example, he says, "He ketched a frog one day, and took him home, and said he cal'lated to educate him." Wheeler is obviously a fixture of Angel's Camp, a good example of a man of the West. But he's good-natured throughout the story, demonstrating great compassion and respect for the "heroes," both animal and human, in his tale.
Twain portrays the two narrators as very different in personality, style, and education, which adds additional humor to his story.