Both boys come from the poorest class in Maycomb. Their fathers seem to be unemployed. The reader knows that Bob Ewell does not have a job, and because of the financial straits that the Cunninghams find themselves in (having to pay Atticus in a non-monetary manner), it is safe to assume that Walter's dad is also without a steady job. Both boys are proud and naturally do not want their poverty brought to light. When Miss Caroline singles out Burris and Walter at different times in front of the class, both are embarrassed. Both characters also seem to be motherless; the author states that Burris's mother is dead, and Walter's mom goes unmentioned in the novel. Thus, their father's play an influential role in their lives.
While both boys come from the same social class, there is a marked difference between them and the manner in which they are raised. Burris's father makes a living off the town's welfare and goodness and does not stress education. Walter's dad deplores being indebted to any man and sees that his children attend school regularly. Burris's father teaches him to be disrespectful and bullish, while Walter's dad can be reasoned with and is willing to admit when he's wrong--the same can be said of Walter.
The author uses the two boys and their families to show that even in the midst of a depression and extreme poverty, one can hold onto his dignity (Walter and his family) instead of regressing to everyman for himself (the Ewell family).