While there are many forms of compare-and-contrast essays, the best ones use the points of comparison and contrast that they identify between the works in order to make a claim about how one text illuminates the other or how they illuminate each other. Rather than a simple delineation of differences and similarities, your essay should use those differences and similarities to make a larger argument about how comparing the two texts reveals some unexpected or non-obvious about one or both of the works.
Most often, such claims work to show how texts do similar things differently. Therefore, often the best structure for this kind of argument is to detail enough similarities between the works (especially works written by vastly different authors and/or in different literary periods) to justify your comparison and to narrow the scope of your discussion. In other words, first show how your two vastly different texts are attempting similar things. Then, focus the remainder of your essay on the nuanced differences between each text’s approach to those similar things and the way in which juxtaposing them illuminates our understanding of one or both.