The key thing with comparison essays is to make sure that the essays do compare the two factors throughout. There are two ways to do this:
1) Compare them directly throughout the essay. For example, if you were comparing how Person A and Person B contributed to Medicine in the Renaissance, you could talk structure one point as follows -
'Person A made an important contribution to the knowledge of anatomy. For example.....(and then write about his contribution)''
'However, Person B's discoveries had a much larger impact on anatomical understanding. For example...(and then write about his impact)
2) The other way to do it is to explain all of your points about Person A first, and then in the second half of your essay write all of your points about Person B. This is the method to choose if their contributions were both very different, in which case the first method wouldn't work too well.
As with all essays, your introduction should quickly summarize what you are going to talk about with a little bit of background. Your conclusion for a comparison essay should sum up each person's contribution, for example, and then asses which factor is the most important.