There is no really wrong or right way to compare and contrast poems. As long as you think through how the poems are alike and how they aren't so alike, you should be fine.
One difference that we immediately noticed was the size of the poems. "Harlem" is much smaller. It's almost like a bite-sized poem. "Theme for English B" has much more lines and many of those lines go on a bit longer than the lines of "Harlem."
The above, we might say, is a difference in structure. Now let's read the actual poems and see how they compare and contrast.
One similarity is that they both start with a prompt. It's like Hughes is responding to a question or assignment. In "Harlem," the prompt is a question: "What happens to a dream deferred?" In "English B," the prompt is an assignment. The instructor tells him to: "Go home and write / a page tonight."
Yet "English B" is more like a story. There's characters, specific settings, and action, we go with Hughes as he crosses St. Nicholas, Eight Avenue, Seventh, and so on. Then we're with him in his room. There's also the character of the instructor. We could probably say that Harlem is a character as well. Hughes treats it like a character when he says, "I feel and see and hear, Harlem, I hear you."
We don't see such characters and specific settings in "Harlem". We can deduce that the poem has something to do with "Harlem," but, unlike in "English B," the poem makes no mention of specific streets or places. Although, in "Harlem," there is action at the end with the emphasis on "explode."
Let's also take a moment to compare the sounds of these poems. We notice that both employ rhyme and alliteration.
In "English B" there's alliteration with "Bessie, bop, or Bach." There's also many examples of rhyme, including: "So will my page be colored that I write? / Being me, it will not be white."
In "Harlem," too, there's alliteration with "syrupy sweet." There's also many noticeable rhymes. Two examples: "sun" and "run" and then "meat" and "sweet."
Perhaps the rhyme and rhythm of the poems tell us something about their themes. How might the narrator in "English B" be like the "raisin" in "Harlem"? We could say both deal with belonging and how to fit or not fit in within a hostile society. Rhymes, too, show us how some words fit together and some don't. Yet in the end, whether they sound alike or not, the words still share the same poem, just as White Americans and Black Americans still share the same country.
The theme of both "Theme for English B" and "Harlem" encompass the difficulty of living in White society as a member of a racial minority. For instance, in "Theme for English B," Hughes states,
Sometimes perhaps you don’t want to be a part of me.
Nor do I often want to be a part of you.
But we are, that’s true!
In "Harlem," he writes about how minority groups have fewer opportunities to realize their dreams when he asks, "What happens to a dream deferred?" This poem also forms the title for Lorraine Hansberry’s famous play about a Black family trying to realize its American dream(s), A Raisin In The Sun.
in "Theme for English B," Hughes compares and contrasts his own life and background with that of white society, telling the reader that
I am twenty-two, colored, born in Winston-Salem.
By comparison, he does not provide any personal information in "Harlem," but speaks in more general terms about the “dream deferred.” Because we know the poem is about deferred or unrealized dreams AND the title is "Harlem," we can infer that Hughes believes that people who live in Harlem see their dreams thwarted more often than the general, non-minority population.
Hughes also uses the neighborhood as a symbol for the reduced opportunities of its minority residents in "Theme for English B." He contrasts himself with the professors and fellow students, just as he contrasts the overall university with the people of Harlem. He attends, "this college on the hill above Harlem." The placement of the college above Harlem implies that the students who attend have greater chances of realizing their dreams than people who reside in Harlem, or minorities, have.
You could take a variety of approaches in analyzing both of Hughes' poems. One approach would be to discuss how both poems discuss the divergent experience of people of color, specifically African- Americans. The exploration of "Theme for English B" is the appropriation of one's own narrative that has convergent elements from the cultural majority and one's own specific experience. This same exploration happens in "Harlem," when Hughes analyzes the results of narratives whose dreams have put aside. At the same time, this might be where a point of divergence might lie. "Theme for English B" presents a vision where one's dreams are accomplished in being true to one's own sense of identity as well as being a part of another world. This vision is not necessarily shared in "Harlem," where one ponders the different and sadly destructive paths are forced to be taken when one's dreams have been continually deferred.
One prewriting strategy that may work for you is the traditional Venn Diagram. Some slangy teachers simply call this type of graphic organizer the "double bubble." Consisting of two interconnected circles, the diagram allows you to place differences between two things on the outside of the circles, and similarities between the two on the inside. I would look over the two poems, and identify at least five things that are different in each, and then find five similarities. It may be helpful to start with the basics -- for instance, both poems are by the same author. That would go in the center, under similarities. Using previous posters' guidance regarding theme and tone may be helpful also. Sometimes just getting ideas into a different form is helpful.
You will want to focus on the following, writing about a paragraph for each:
Speaker's Tone/Attitude: do both poems use a young black male speaker? To what effect? Is his voice plain, sarcastic, dejected, angry? Why?
Imagery/Metaphor: to what images, symbols, and metaphorical things does the speaker compare his predicament?
Style: why does the speaker use free verse style? Are there musical/metrical qualities to the verse? Why so many rhetorical questions? What are the implied answers to these questions?
Theme: Are the themes racial only? What do they suggest about the socio-economic and racial relations in America at that time? In the educational system? Is America and its schools the land of opportunity?