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.