Of course the Stanford academic brand is stronger.
But I'm doubtful that the actual undergrad education is always better. Again, professors > grad students and ample research opportunities > little research opportunities.
There's a reason strong liberal arts colleges continue to flourish all around the country, enrolling students who are also getting into more national brand schools. BYU is sort of like that, but weaker in the arts, stronger in the sciences and with a massive helping of cultural impetus for attendance.