Compare the Easiest
Initially compare the easiest, the most obvious descriptions of characters. Write about their age, origin, education, social status and material prosperity. Pay attention to the features of their nature. One main character can be romantic, funny and honest. Others may be cynical and have a habit to deceive.
Behavior and Attitude to Others
Do not forget to mention their attitude to life and people, for example, to those who surround them. One can be tired of living (Hamlet), the other keeps on cognizing it without any weekends (Faust). One can understand every other person (Sancho Panza), the other thinks only about himself (Don Quixote). It is quite important to compare how characters behave in the same situation. For example, during the time of war Andrew Bolkonsky ("War and Peace") signs up to be a soldier in an army in the field, Pierre Bezukhov becomes a member of the emergency volunteer corps.
Tatyana Larina ("Eugene Onegin") is 18. She was born in the landlord's family, grew up in a village. Tatyana was brought up by the nurse, who really loved her. She is beautiful, romantic, thoughtful, naive, because she does not know a lot about life, but she reads a lot of French novels. Anna Karenina is a young and beautiful lady who is originally aristocratic. She is used to going out, to meeting different people but she is also still naive and trustful. Both of them are quick to fall in love when they meet someone who differs from those they always see in their surroundings. Both of them do not hide their feeling and are ready to follow their chosen one. Here is an example of the character's behavior in the similar situations. Tatyana Larina stays true and faithful to her husband even after Onegin has proposed her his love. This choice helped her to save her honor and dignity. On the other side, Anna Karenina counted that love is more important than marriage. This choice ruined everything. She could not stand living with a person she did not love. Consequently, she committed suicide.
Worldview and Your Opinion
It is also important not to forget to compare the worldview and the philosophical positions of the characters. One can be more altruistic and moral. The other may be Nietzsche's follower and believe only in himself. Write about their relationships with other characters. Be attentive to what an author tells you about the characters. How does the author describe them: with love, with surprise or with ignorance? Which feelings does the author want to awake in the reader with such descriptions? Finally, define, what you think about those characters and let your reader feel it, too.