My son got a Presidential at the U because it is based on grades, class difficulty and test scores - which is his strength. Plus he got a bunch of other scholarships.
He was also a finalist for the Monson Scholarship. As you may already know, after the pool of Monson candidates has been established - they ignore the grades and look at service and leadership. My son was relatively weak (compared to that pool of candidates) in service. He didn't win state as a Sterling Scholar for the same reason.
Just another example of Utah and BYU being different.
Just for kicks and giggles, I will give you 1 more difference. This son lived on campus in the housing that was used for the Olympics. They did tons of missionary work with a group of RMs and they were baptizing a convert into their student ward almost EVERY WEEK. Very very cool and I have never heard of that at BYU.