This structure focuses on the comparison and contrast instead of on the two ideas (e.g., corsetry and footbinding) being compared and contrasted. If you begin with the comparison, then the contrast will get emphasis - the logical movement is from thinking about similarities to thinking about differences.
This method is probably the one used most commonly.
A quick outline comparing and then contrasting corsets and footbinding shows one way that such a paper might be structured.
Comparing refers to features that your subjects have in common (like two fast food places), and the contrasting refers to their differences (one sells hamburgers while the other sells fried chicken).
The subject you choose in your essay must be something that is similar in type, but different in characteristics.
Somewhere in your essay you should take the approach of showing two contrasting views regarding your subject.
If you are arguing that the fried chicken joint is better than the hamburger place, include a different side to that opinion by furnishing the reader with information from another source. Feel free to state your own opinion, and then mention that some do differ with it.
This means that you should try and fit as much of the above factors in as you can, without going over your word count.
If you stick to the basic guidelines stated here, you will render a very interesting compare & contrast essay.
A structure like this one seems more focused on the ideas being compared and contrasted than on the comparison and contrast itself.
The similarities and differences between the ideas do not begin to emerge until the writer gets to the second idea.