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.