no conscious intention of openly rebelling against this situation, but when he goes to work for the Daltons, events overtake him, and he's essentially trapped into circumstances where the killing of Mary Dalton is the result. From that point, he is a man on the run, emblematic of the outsider status of African Americans. His understanding of the oppressive US racial dynamic becomes increasingly objectified and explicit. While he is on the run, his killing of his girlfriend Bessie, though horribly cruel and completely unjustified, can perhaps be seen as symbolic, in a very misguided way, of his resentment of other black people, who apparently do not want to face the same facts of which Bigger is aware.

In The Outsider, Cross Damon is a far more mature person than Bigger but, at the start of the novel, is similarly in conflict with the white society and with his own mother, his ex-wife and his girlfriend. A subway accident allows him to stage his own death and assume a new identity. In moving to New York and becoming part of a Communist "cell," he is able to observe that even these white people who claim to be fighting for the rights of African Americans are largely hypocrites and are interested only in power. Cross's new identity has become one of experimentation, of freeing himself from the conventional morality burdening and controlling everyone, but especially black people. At the end, he is shot by the communists and, on his deathbed, tells the D.A. Ely Houston, who had become a kind of friend to Cross, that he was on a quest for knowledge and freedom, but that he had found "nothing. The search can't be done alone."

In both these works, Wright presents a realistic and violent struggle against the oppressive forces of US society. Tragically, both Bigger and Cross are misguided in their methods of carrying out the struggle, though this itself is emblematic of the fact that African Americans of that period were essentially trapped—without the means yet to achieve victory.

Langston Hughes, in his poetry, deals with the same facts of African Americans who are fighting, in their own ways, against oppression, but without violence and obvious hatred. In some cases, his poems simply express a feeling of isolation and sadness, but also a joy in those things an oppressed people are still capable of being fulfilled by:

To fling my arms wide
In some place of the sun,
To whirl and to dance
Till the white day is done.

In poetry, a thought which a novelist needs 300 pages to express can be encapsulated in a few lines. In the work of both Wright and Hughes, the underlying theme is not simply oppression but the exclusion of black people from America—not just physical exclusion from "whites only" places and jobs, but the exclusion from the concept on which the country was intended to be founded.

I swear to the Lord,
I still can't see,
Why democracy means
Everybody but me.

Hughes's poetic speakers are at least apparently more light-hearted and optimistic than Wright's. When Alberta Johnson is having her calling cards printed, the dialogue with the printer goes,

Shall I use Old English
Or a Roman letter?
I said, Use American.
American's better.
There's nothing foreign
To my pedigree:
Alberta K. Johnson—
American, that's me.

Alberta, and Hughes, are making the point, which should be self-evident, that African Americans are as American as, if not more so than, everybody else. It is stated with a confidence that essentially proves true something which should not have needed "proof."

Though Wright and Hughes deal essentially with the same themes, Hughes's overall tone, as stated, is frequently "lighter," more direct and succinct. Hughes explores the same feelings and situations as Wright, and, at times, describes the same violence, as in his poem that describes a lynching. Wright, however, generally has a darker, more existentialist tone in his writing. In Wright's short story "The Man who Lived Underground," the protagonist is shot to death by the police, essentially the fate Bigger Thomas and Cross Damon end up suffering in different ways. Wright's central characters struggle and lose, though achieving something in the process. Hughes's more often than not are victorious in their expressions of truth.

To answer this question fully, I think it would be necessary to compare and contrast specific works. I don't have such works on hand at the moment, but I'm confident that I can make a generalization or two.

The two writers both address racial discimination in the early 20th century, but they do so in different ways. Hughes is well known for his use of humor and subtle irony, his technigue, as he calls it in more than one place, of "laughing to keep from crying." Wiright, on the other hand, tends to be open and direct in his criticism. His works are often filled with a sense of righteous anger. Both are good writers, I think, and both are important figures in African American literature.

As a side note, you may be interested in reading more about the connections and differences between Hughes and Wright. One place to start would be their different biographies. Another place would be Hughes' essay "The Negro Artist and the Racial Mountain" and Wright's essay "Blueprint for Negro Writing." The two writers express here their different views on black identity in the United States.

This is a fairly broad question.  I mean, there is no earthly way the space here on eNotes will allow a sufficient discussion of such an intense topic.  I do think that both Hughes and Wright spend a great deal of time exploring the condition of power in America.  They both focus on this in specific terms with the African- American condition and how power, or the lack of it, is a part of this reality.  I think that Wright 's association with Communism and the emphasis on socio- economic reality is something that truly drives his work.  For example, Dave in "The Man Who Was Almost a Man," is marginalized both economically and socially in that he is a poor young man of color.  Both race and class play a role in his silencing, and Wright forces the reader to examine both conditions critically.  This is something that is present in Hughes, but not in as dominant of a form.  Hughes focuses on the condition of African- Americans in a paradigm of how dreams and opportunities are continually denied or "deferred" to them.  In this vein, economics is a part of such a process, but it seems to me that Hughes is more interested in exploring a condition where dreams on many levels, economics being one of several, are denied or deferred, whereas with Wright, this condition is something rooted in both economics and race.  This comes out in their style of writing in that the prose of Wright is centered on the discussion of race and class.  Characters and condition emerge in his prose where there is both an artistic and an sociological analysis present, compelling the reader to analyze situations presented in the prose.  For Hughes, the complexity of dreams and their effect on the individual is widened in the idea of poetic exploration, which is not necessarily defined in one domain or realm but something, like poetry in general, can be explored in many different ways with many different approaches.  Their respective differences in style, in this instance, could be reflective of their different approaches to discussing the issue of race in America of the 20th Century.