We should begin our comparison by noting that Paul Laurence Dunbar uses traditional poetic structures much more frequently than Langston Hughes does. This isn't surprising, given that Dunbar was a generation older and wrote most of his work during what was still the late Victorian period. "The Haunted Oak," for example, is written in four-line stanzas, with the rhyme scheme ABCB. "The Debt" is written in similar quatrains, with the rhyme scheme AABB. Hughes, on the other hand, uses freer poetic structures, with less regular meter and rhyme, as one would expect for a poet writing during the modernist period in the twentieth century.
One could say this is a superficial distinction between the two poets, but it has an analogue in their subject matter and the manner in which it is dealt with. Both poets deal with racial injustice and the oppression of African Americans. But Hughes's way of expressing this theme is bolder. A poem such as "Let America be America Again" describes the dysfunctional racial dynamic of the United States more clearly and explicitly than any poem of Dunbar (or any other of Hughes himself). There is also a more direct sensuality in Hughes's verse—unsurprisingly, given that Dunbar died in 1906, and open and frank discussions of sexuality were not considered proper in his time.
That said, many readers judge Dunbar's poetry to be more lyrical than that of Hughes. A separate issue is the fact that Dunbar uses the dialect of African American speakers more frequently than Hughes. Unfortunately, some readers may interpret this aspect of Dunbar's technique as inadvertently reinforcing stereotypes. The standards of his time regarding the use of non-standard language in literature were different from ours.
Both Dunbar and Hughes perhaps have much more in common, however, than one would think from a casual reading of their poetry. Both were ahead of their time and were path-breakers in giving voice to the African American experience in a highly expressive way.