Linking of A and B. For instance, in a paper asking how the "discourse of domesticity" has been used in the abortion debate, the grounds for comparison are obvious; the issue has two conflicting sides, pro-choice and pro-life.
Point-by-point Rather than addressing things one subject at a time, you may wish to talk about one point of comparison at a time. To use the alternating method, you just need to have something noteworthy to say about both A and B in each area.
If you are a visual person, a Venn diagram can facilitate this process.
Create a thesis statement that reflects their relative weights. What kinds of governments were there? Pay attention, too, to the use of words and phrases that juxtapose or suggest comparison.
This relationship is at the heart of any compare-and-contrast paper. Be aware, too, of the placement of your different points.