There are more than two ways to organize a comparison/contrast essay. Some of the better academic writing software out there will probably give you at least five as part of their guides. However, these two offer the most common and, in many people’s opinion, the most intuitive ways to present them.
Subject-by-subject. In this style of organization, you begin by discussing the first subject, detailing all the points you want to make. After completing your spiel, you move on to the second, discussing ideas and characteristics in parallel.
This style of organization is often best used for “lens-type comparisons,” where you draw out information about your main topic using a different one. Typically, you’d like your primary subject to go on the second part of the essay to make it easier for the reader to remember.
Point-by-point. Here, you tackle the objects together, arranging your discussion according to the points you’re comparing. For points where you’ll have much to say, you can devote an entire sentence to each. You can also combine related ones to if your resulting discussion will be shorter.
One of the most important things to remember is that the last point you make in each paragraph is ultimately what you leave your reader. If you want to push the similarity between the two objects in question, then end with that; same with the differences.