In A Raisin in the Sun, how do the two men interested in Beneatha represent conflicting dreams of the characters in the play?
This is a great question because it shows that you have identified how George and Asagai respectively represent two different approaches to being African-American in the play. Perhaps the conflict between these two different views is highlighted most clearly by George when he comes to pick up Beneatha to take her out and finds that she has cut her hair short and let it be curly, rather than straightening it and keeping it long. This of course is thanks to Asagai's influence in encouraging Beneatha to embrace her African roots and not assimilate. Note how George responds to this statement of Beneatha's and her comment about assimilationist Negroes:
Oh dear, dear, dear! Here we go! A lecture on the African past" On our Great West African Heritage! In one second we will hear all about the great Ashanti empires; the great Songhay civilisations; and the great sculpture of Benin--and then some poetry in the Bantu--and the whole monologue will end with the word heritage! (Nastily) Let's face it, baby, your heritage is nothing but a bunch of raggedy-assed spirituals and some grass huts!
Asagai represents Afro-Americans who are trying to reconnect with their African "heritage," rejecting the customs of the white majority. George is a man who has made a success of himself by deliberately learning how to be successful in the white world. As Walter says, he has studied the ways of the white man, and is successful by acting "white," and following the laws and customs of the most powerful majority, rather than rejecting them and trying to be successful in his own right.