When you are assigned an essay comparing and contrasting two poems, you should start by thinking about what you can legitimately cover in the word or page count specified by your instructor.
You might start by examining the formal qualities of the poems. Are they both in regular meter? If so, do they use similar or different prosodic schemes? What salient features are similar and different in the forms of the two poems? Next, look at style. Do they use figures of speech in similar ways? level of diction -- is one more colloquial and one more formal?)
Next, look at point of view. Are the poems first or third person? How do the viewpoints and narrative voices differ or are they similar?
Consider genre, emotional tenor and tone next, whether the poems are comic or serious, joyful or sad, etc.
Finally, address subject matter.
Basic Structure: Depending on the length of the piece you need to create, there are a number of ways to address compare/contrast. The basic rules of essay or paper writing will still apply. Make sure you have a clear, concise thesis, with a plan statement, well thought out body paragraphs with plenty of support for every topic you choose to cover and a thorough conclusion. Above all, be certain to compare apples to apples. In other words, if you point out one author's use of allusion, you must, at some point also discuss the other author's use of allusion.
Content: You may wish to start with the authors. Who are they? Where are they from? What is there about their life experiences that caused them to write as they did? In short, what influence did their cultural experience have on the poems under disucssion?
You might then go on to discuss the two author's use of literary elements. For a shorter piece, you could choose one, such as imagery. Do they authors use one type, or all five? Are the images graphic or soft focus? How does this affect the tone or mood of the poems in question?
For a longer piece you might select several elements, such as irony, allusion, simile and metaphor, hyperbole, tone, mood, rhyme, meter, etc. and do a paragraph analyzing the two author's use of each. Which direction you go would, again, depend a great deal on the length of the comparision. If you are limited to an essay length of one to two pages, you would have to choose fewer topics, but if you have more space, you can go into more detail.
Organization: it is important that you are consistant through out. In other words, whatever organizational type you choose, whether stanza by stanza, topic by topic or author by author, stick with it from start to finish. Your organizational structure should be telegraphed by your plan statement. It is confusing to a reader if you begin by discussing the first stanza of each poem, and then go on to each author's overall use of imagery in the second body paragraph.
For the sake of clarity I would suggest either a poem centric or a topic centric organization. For instance, if you were to choose a poem centric structure, you would want to discuss all aspects of poem one, and then discuss all the SAME aspects of poem two before bringing them together in the conclusion. This might work well for a longer paper where you can do several paragraphs on each poem.
Alternately, you might choose a topic centric organization. In this structure you will discuss both poems in each paragraph, but limit yourself to a single topic such as allusions or imagery for each paragraph. This second option is, perhaps, the easier and clearer of the two.
Whatever structure and organizational path you choose, remember to fully support every statement with examples, quotes and explanations. Half supported generally equals low marks.