When comparing two characters in a work of literature, start with how they are different. Often times the differences are easier to see. Look at how they respond to other characters in the book, how they react to things happening in their own lives, etc. While superficial comparisons are decent, the better comparisons are those that look at emotions of characters rather than just what they say or how they are portrayed to look in a literary work.
Once you have found a few differences, take a look at the characters similarities. You may have stumbled upon a few when you were looking for differences earlier, so don't forget those! Otherwise, don't be afraid to look toward the very specific details about a character to find similarities. Often times, characters might be different in their opinions on a certain topic, but even though they have varying opinions, they might be both looking toward the goodwill of a fellow character. Don't be afraid to look at each character through their own eyes. A situation that looks different at first can be similar under the surface.
Try using a Venn Diagram to organize your thoughts about the characters. On the two circles, write things about each character individually. On the overlapping section, write down things that seem to be inherent in both characters. Using a graphic organizer often times helps me organize my thoughts a bit better. I have attached a link to a Venn Diagram for you below. Hope this helps!
eNotes offers a free guide called "How to Write a Compare-and-Contrast Essay". Please see the link below for more information.