Both of these novels are also examples of a bildungsroman, which means a novel of education or development. They focus on a single character, and, by charting this character's life from their childhood through the struggles of growing up and adulthood, show how the character matures and develops through facing various trials and struggles. Bildungsroman novels normally end with the older, wiser narrator assuming a place in society. These elements are clear in both of these novels, so you might wish to compare the way in which Dickens shows the development of the two central characters, and the sufferings they need to go through to get there.
These are two excellent novels to compare, because both are semiautobiographical, but they represent different views of Dickens's life. David Copperfield is optimistic, and was written when Dickens was younger. Note that David starts out in a higher social class, is reduced down, and then returns due to his own merit. In Great Expectations, the same thing happens except that Pip has no talent and everything is handed to him. It is an interesting perspective on Dickens's life, and much more somber.