Why, in your opinion, does Twain include a description of the circus in Chapter 22 of The Adventures of Huckleberry Finn?
How would you compare the circus with the entertainment provided by the duke and the king?
The two separate questions you ask here are intricately connected: the circus description is included expressly to compare with the entertainment provided by the duke and the king. Huck is incredibly impressed by the "real bully circus." He describes it as "the spendidest sight that ever was" as he sees the ladies riding in on horses "dressed in clothes that cost millions of dollars" and other ornaments that were just "littered with diamonds." He is even impressed with the "drunk" that eventually becomes part of the show as a skilled rider. Conversely, the entertainment of the duke and the king have the opposite effect:
That night we had our show; but there warn't only about twelve people there--just enough to pay expenses. And they laughed all the time, and that made the duke mad. (149)
The king and the duke make excuses saying that "these Arkansaw lunkheads" weren't smart enough for Shakespeare, so a low comedy was what they needed (149). Here's a hint: it wasn't the people of the town that were the "lunkheads." Ha! In order for the townspeople not to seem foolish, they pretend to like the show (which ends up consisting of random antics on the stage).
In regardst to comparisons, the circus is truly a good circus; however, the entertainment of the king and the duke is a "circus" in the worst sense of the word. It is a comparison of high quality circus entertainment to low quality theater.