The first thing I would do when asked to compare and contrast the two novels would be to consider the main elements of each story. For example, list elements such as setting, antagonist, protagonist, theme, etc. Then, jot down a few things about each of those elements as it pertains to each story; the protagonist of To Kill a Mockingbird can be compared to the protagonist of The Hunger Games because both are young, female, stubborn, outspoken, and have only one living parent and one sibling. On the other hand, the two can be contrasted based on fact such as Scout's being the younger sibling, while Katniss is the older, etc.
In each of the books, the protagonist must face a society that is harsh in many ways. However, both characters learn to rely on their strengths to make it through the hardships with which they are faced. Each of the learns to persevere and that judgment of others without knowledge of them is not wise.