When do I use the alternating method? Professors often like the alternating system because it generally does a better job of highlighting similarities and differences by juxtaposing your points about A and B. It also tends to produce a more tightly integrated and analytical paper. Consider the alternating method if you are able to identify clearly related points between A and B. Otherwise, if you attempt to impose the alternating method, you will probably find it counterproductive.
While your emphasis in a Comparative essay is based in the main body of your essay, your introduction and conclusion are important too. For the sake of maintaining simplicity in your Comparative essay, it is wise to keep your introduction as short as possible. You could introduce your objective for comparison and state which topics you are going to compare. If there is any main claim or point to make, you should do it towards the end of your introduction. This will serve as your thesis statement, which will be recalled or re-stated in the conclusion.