When you compare and contrast two different stories, you are identifying ways in which the stories are similar and ways in which they are different. There are two basic ways of organizing the points you will make in your essay.
1. First, list all the similarities between the stories, including illustrations to support your points. If the main characters of both stories have similar personality characteristics, you might use a quote from each story to show the resemblance. Work through the list, mentioning one similarity at a time and showing how it is present in both stories. Then, list all the ways in which the stories have differences, referring to one contrast at a time and providing examples from each of your stories. This could be called an "alternating" approach.
2. You could present all your information about one story, then all the contrasting information from the other. If you use this approach, you would present and/or explain features from one story and then present and/or explain equivalent features from the other, pointing out how they parallel or differ from the first story. This is the "tandem" approach.
Either way of organizing your information is valid. The "best" way is whichever approach allows you to comfortably and clearly explain how the stories are the same and how they are different.