Biff and Happy each follow Willy's example growing up, believing that they are bound and destined for greatness and that anything less than being loved by everyone and hugely wealthy will constitute failure.
Biff is the older brother, the more talented brother, and the more intelligent brother. Though it is tempting to say that he is also the more troubled of the two brothers, Happy presents a deeply troubled personality in the play.
Happy is overlooked, perhaps justifiably, and simply has less potential than Biff. Yet Happy stays close to Linda and Willy, seeking their approval and affections. He loses their respect through his womanizing and his frivolous antics, which can be seen as a simple and direct psychological extension of his need for approval.
To the end Happy remains convinced of Willy's dream, speaking at Willy's funeral about the quality of the dream, its truth and its nobility. Happy's need for Willy's approval seems here nearly pathological as he pledges to continue Willy's legacy, completely ignoring that fact that Willy's dream led him to suicide.
"I'm gonna show you and everybody else that Willy Loman did not die in vain. He had a good dream. It's the only dream you can have—to come out number-one man. He fought it out here, and this is where I'm gonna win it for him."
Unlike Happy, Biff comes to realize that he has been foolish to follow Willy's example and to believe in Willy's dream of greatness. Biff does not have greatness in him, he discovers in a moment of true honesty. He is not a bad person, but he is also not great and never will be.
Biff effectively wakes up after he is denied a loan from his former boss. He realizes who he is. He attempts to share this realization with his father.
"You were never anything but a hard-working drummer who landed in the ash can like all the rest of them! ... I'm nothing, Pop. Can't you understand that? There's no spite in it any more. I'm just what I am, that's all."
Willy is unwilling or unable to accept this new truth from Biff and persists in his delusional dream, going so far as to commit suicide to avoid dying as a complete failure. If Willy were to listen to Biff and face reality, he might see that he has not completely failed in the world. He has raised two children and paid off a house. He has a loving wife.
Yet Willy is attached to the dream represented by his brother Ben, the dream of greatness. It is this dream that captures Happy and dooms him to a fate like Willy's. It is this dream, ultimately, that separates the brothers and sets them apart as Biff turns away from the fantasy that afflicted his father, embracing a humble honesty instead.
Early in the play, Arthur Miller provides a description of Biff and Happy Loman in which he compares and contrasts the brothers. They are both upstairs in the bedroom they shared as kids.
Biff is two years older than his brother Happy, well built, but in these days bears a worn air and seems less self-assured. He has succeeded less, and his dreams are stronger and less acceptable than Happy's. Happy is tall, powerfully made. Sexuality is like a visible color on him, or a scent that many women have discovered. He, like his brother, is lost, but in a different way, for he has never allowed himself to turn his face toward defeat and is thus more confused and hard-skinned, although seemingly more content.
Both brothers are "lost." Happy seems more content with his lot in life than Biff. This may be because Happy is an extreme womanizer and highly successful at that. Biff has a worn air and seems less self-assured than Happy. This is probably because Biff was obviously his father's favorite and is now stuck with the task of trying to live up to his father's expectations. Arthur Miller seems to be a shrewd judge of human character. He reads a lot into people. His characterizations are subtle. Happy does not seem like such a complex character to a person viewing or reading the play. It would be easy to feel that Happy is just happy-go-lucky, as his name implies. But he is, according to the playwright, more confused and hard-skinned than Biff. This suggests that Happy will always be confused because he won't face reality, and that Biff will eventually find himself because he is under stronger internal and external pressure to do so. Happy seems to have bought into his father's American Dream and to be fated to end up more or less like his old man after his sexual appetite diminishes and his attractiveness to women wears off. What seems to be the most important characteristic of both brothers is that they are "lost." They haven't found themselves. They don't have direction in their lives. They have never prepared for any kind of careers, and consequently they are underachievers. This may explain why neither has ever married, although Biff would be thirty-four and Happy thirty-two. If either of them did get married he would be a poor provider. Happy would be unfaithful. Biff would never earn much money. Miller does not suggest what Biff's "stronger" dreams are, but it will come out in the course of the play that he dreams about living and working in the open country and escaping from life in the big-city. Both brothers, of course, are disappointments to Willy, who thought so highly of himself that he automatically assumed any boys he fathered would be successful in the greatest country in the world. Willy is largely responsible for the fact that both sons seem lost. He has been a poor role model, and his job as a traveling salesman has keep him away from home much of the time.