Which do you think is more important? For example, if one wanted to major in some aspect of business, would it be better for them to go to Indiana University, a school with a highly reputable business program, or to go to Brown University, a more reputable school with a less reputable program than Indiana? Or for engineering, would it be better to go to a renowned engineering school (UIUC) or a school with a better program (University of Minnesota for Chemical Engineering). Does one factor matter than the other?
Sometimes these factors can coincide. But mostly, you want to go for quality of education not quality of name.
There’s no clear answer. It really depends on a lot of factors. Certainly IU has a great business program. And naturally, many that are knowledgeable of business programs would be aware of its quality. But if your goal was to live / work in the northeast or Wall street, it might be better to go to Brown. But this is assuming a number of things, like admittance into both schools. (Brown has a single digit admissions rate IIRC.) Also, many would only recommend IU if you were a resident of Indiana. If you weren’t, they might recommend a more local option. And furthermore, an applicant capable of getting accepted into Brown is also capable of getting accepted into a number of other high quality schools. And these schools will likely have great business programs.
With UIUC and UMinn, whichever you’re a state resident of would probably be the one that’s recommended, assuming financial aid packages aren’t similar. So, it’s a lot of ‘it depends.’
I tend to advocate that a high school senior choose a school based on its overall quality (assuming the school has a well developed program in the area of interest) rather than the ranking of a particular program unless the student has shown extreme interest in a particular field. The reality is, the vast majority of college graduates changed their major at least once, and many do it many more times.
While some switch to closely related fields like geology to geophysics or English to comparative literature, a huge number change to something completely different. Often this is because they lacked real exposure to the subject in high school. For instance, intro US history courses at a rigorous school are far different than AP US History, so a student who loved APUS might find he hates real college level history courses and vice versa. Other students may discover that they enjoy a subject they had barely even heard about in high school. For instance, if you asked most people what geography majors do, they’d likely respond by hesitating and tentatively asking, memorizing the state capitals? The reality is far different but a student might not know this until he takes a geography course for a gen ed.