Willy has a different relationship with each of his sons. With Biff, Willy is hopeful and adoring, yet also defensive, judgemental and combative. With Happy, Willy is dismissive and disinterested.
Biff is the son with potential in Willy's eyes. Biff plays football as a child and excels. Biff praises Willy, looks up to him, and wants to be just like him when he grows up.
Crisis comes when Biff catches Willy with a woman in Boston. Biff cannot forgive Willy for letting him down and betraying his mother. This leads Biff to fail (he fails to graduate college, gets fired from his job for stealing, and generally fails to establish himself as an adult).
Biff is tortured by his disillusionment with Willy, by his failure to live up to his own standards, by his failure to achieve the greatness that Willy dreamed he would...
Willy fears Biff's judgement and expresses this fear by lashing out at Biff, yet Willy cannot fully let go of his hopes for Biff. He longs to see Biff achieve the greatness he failed to achieve himself. This conflicted relationship is maintained throughout a majority of the play until Biff finally determines to forgive and to end the cycle of conflict with his father.
"There's no spite in it any more. I'm just what I am, that's all."
Happy and Willy have a less animated relationship. Happy is largely invisible to Willy, though the tries repeatedly to gain his father's attention and to become worthy of his father's adoration. Not getting these things from his father, Happy becomes a "womanizer" and seeks affections elsewhere.
Yet it is Happy who staunchly defends Willy's failures as if they were successes. It is Happy who proclaims that Willy was a great man.