A Raisin in the Sun's characters of Asagai and Murchison are, as the previous posts noted, very different. The way they differ from each other makes them a kind of character that we call a "foil." A foil is a character that illuminates the important traits of another character by contrasting with them.
Asagai appears to the ideal black man in terms of his ability to deal with being black in America. Ironically, he is not American, and that is probably what gives him his unique perspective. He still has a close connection with Africa and the identity it gives him.
Murchison, however, is trying to function as a black man in a white man's world. It leads him to feel scorn for others, such as Walter, who are struggling to establish their identity on their own terms, instead of trying to mirror white society.
Asagai is portrayed in a much more positive light. We see him as strong, independent, and wise. The female characters are drawn to him. Murchison is whiny and shallow. None of the family particularly care for him, even Beneatha, who is dating him.
Hansberry uses the characters to examine two extremes in the black experience in America. It's obvious which one she values the most. The Youngers fall somewhere in between the two. By the end of the play, they have insisted on establishing their own identity on their own terms, even if it leads to trouble. They have moved in Asagai's direction.
One of the most significant differences is how these two characters see themselves. George is an assimilationist. He acts white, embraces white values, and even dresses like a white man, down to his "faggotty white shoes." The theme of identity is central to the play, and George seems to be trying to reinvent himself as something he is not. He is ambitious, materialistic, and self-centered.
Asagai is proud of his heritage, but he doesn't make any particular effort to prove to others who he really is. And by the same token, he believes that service to others is a worthy, worthwhile thing, in contrast to George's materialism. Asagai is not afraid of being different; he would be one to embrace what we now call "diversity.
The two men are exact opposites from one another.
Joseph Asagai is from Nigeria and encourages Beneatha to be proud of her African heritage, such as letting her hair grow naturally rather than straightening it. He wants black Americans to embrace their roots and not be afraid of showing where they come from. He does still have old-fashioned ideas about a women, however. He doesn't think women should be independent from a man.
George Murchison is from a wealthy black American family. He doesn't care about his African roots or heritage. He feels money and education is the only way to be successful. He's very concerned about outward appearances and behaving properly in white society.