In "Death of a Salesman," how are Willy and Biff's explanations different for Biff's failure to succeed in the business world?

I would only add two things to the first post which covers it pretty well.  Willie has always needed Biff to succeed, particularly after the Boston incident, because Willie thinks that Biff is falling apart because of Willie's "affair."  He needs Biff to succeed in spit of what he has learned about his father, almost as an act of forgiveness.  Biff's learned that his Dad is human; this is a difficult thing for any son to learn about his father.  However Biff had failed because he believed the same dream that Willie believed ... that the cult of personality was what really counted in this world, not performance; that he would be passed in algebra rather than pass it himself.

I also don't know that Willie consciously decides that he can no longer live a life of illusion; I'm not sure that Willie ever achieved that level of self-awareness.  He had been thinking of/trying to kill himself over time because he was a failure, and he had learned the horrible lesson that a man IS a piece of fruit; that you can eat the fruit and throw away the peel.  Who knows if Willie was ever a good salesmen; the evidence seems to indicate that he was not.  And perhaps more important than work, he had failed his son because Biff was never the same after Boston. It's not far from realizing that you're a peel to a total sense of hopelessness.