As a male, I have a slightly different slant on this. As a teacher, I have seen lots of "Biff" over the years ... especially the "star" athletes who received special treatment in almost all aspects of school life ... and please, this is not a general statement about all star athletes, just something I have seen in too many cases. It seems, because we don't know enough to judge, that Bernard was a naturally better student; we know this becuase we have the evidence of his success in law school. Again, there is only "circumstantial" evidence that Biff was not a good student; he regularly needed help ... but this could be caused by any number of things.
The one thing that we know is different between the two is that Bernard did not catch his father in an affair with a stranger; I think this is the turning point in Bieff's life. Biff had so much faith in and admiration for Willy that finding him with a woman other than his mother wrecked his life, killed his chance of going to summer school, getting the credit he needed, and attending college. It's possible that, without this incident, Biff might have had a life with at least some of the success that Bernard enjoyed. Who knows. What we do know is that the trip to Boston contaminated the rest of Biff's life and Bernard had no such reality to deal with.
Toward the end of the play, Willie Loman can't understand why Bernard has grown up to achieve such great success, while Biff's life has been one failure after another. The contrast between the two men, once boyhood friends, is indeed pronounced. Biff is a compulsive thief who can't hold a job, while Bernard is an attorney about to argue a case before the U.S. Supreme Court. Willy can't understand how the two turned out as they had because Biff's failures reflected his father's own flawed values.
Biff grew up as a favored son, star athlete and charmer. He was very popular--one of his father's definitions of success. Biff did not value education because he was not expected to succeed in the class room. Learning wasn't important; making passing grades of any sort was the objective, and Biff's cheating in school was not only acceptable to Willy, it was encouraged.
Biff was never held responsible for his actions: cheating, stealing, making fun of his teacher--all were evidence to Willy that Biff was "sharp," clever, and entertaining. When others held Biff accountable, Willy blamed them, not his son. When Biff failed math and would not graduate, Willy immediately blamed Bernard who must not have given Biff the answers. Nothing was ever Biff's fault, and Biff was, of course, popular.
Bernard, in contrast, was not charming or entertaining. He was not popular. He was, however, an excellent student who worked hard in high school, and after graduation, he excelled academically in college and law school. After he graduated from law school, his career flourished. Bernard also married and started a family. His life was successful in every way, but he felt no need to boast about how much he had accomplished. He did not mention to Willy, for example, that he would appear before the Supreme Court. Bernard's father was justifiably proud of his son. Obviously, Bernard was raised with a very different set of values than those imparted to Biff by his father.