Read the articles several times to ensure comprehension. Take notes when you read so that you can easily return to sections that you wish to analyze or sections you do not fully understand.
Ask yourself critical questions about each article. Consider whether each article provides sufficient research and evidence to support its claims. Other important things to analyze include whether the article makes assumptions, whether there are gaps or questions the author leaves unanswered, whether there is a noticeable bias and whether the article considers alternative points of view and exceptions. Make point form notes about how each article stands up to these questions.
Draft a list of similarities and differences between the rhetorical strategies and conclusions of the two articles. You may be analyzing two articles that reach the same conclusion through different means or you may be analyzing two articles that reach opposing conclusions through similar means.
Make a judgment about the relationship between the articles based on your readings, notes and your analysis of their rhetorical similarities and differences. You may find that the articles complement one another, that they are in dialogue with one another or that they contradict one another. You may also find that one article is more convincing than the other.
Draft your thesis. It will likely take several attempts to write a thesis that is complex enough, yet workable for your paper. Remember that a strong thesis statement contains an argument, not merely an observation. Your comparative thesis statement will present an argument about the articles based on your analysis of their rhetorical strategies. For example: While Article X and Article Y both reach the conclusion that A has a positive impact on B, Article X's analysis is far deeper and less biased than Article Y which relies more on personal conjecture rather than factual evidence.
Create an outline of the evidence you will use to support your thesis statement to ensure that you have enough support for your argument. Tweak your thesis statement as necessary until you have a claim that you feel you can argue convincingly.
Ask friends or your professor to review your thesis. Check to make sure that they understand your main points and to ensure that your thesis is well stated. Revise the thesis as necessary.