Well, it’s a trick question, because no single thing is more important than the other.
Visa Officers look at the totality of your case. Every single applicant has hurdles and highlights, some have more hurdles and some have more highlights. The key to the visa interview is learning how to present your entire case - both the hurdles and the highlights - in a way that makes sense to the Visa Officer and showcases you as an applicant. A Visa Officer isn’t denying your university. They also aren’t denying your sponsor, or your test scores.
They are denying you as an applicant. Of course your university, sponsor, and test scores, all make up who you are as an applicant, but it is important to understand there is a difference. When you, as an applicant, are presenting your situation in the visa interview, you need to present yourself (which includes the components in your case) to the Visa Officer so that they can make a decision on your case.
For an F-1 visa, they then must decide: Is this applicant qualified for this visa? Are they going to use this visa properly? Is there any fraudulent or illegal activity happening here? Then, they will make a decision.
Your presentation of yourself all contributes to their understanding of how you as an applicant fit into those questions.
So, if you are denied your F-1 visa when you apply again, changing your school from one college to another of the same level will likely not help you, nor will changing your sponsor from one person to another with equal funds. The visa interview is not simply checking boxes and answering questions, it is a conversation with a U.S. government official to determine that you are qualified for the visa and will use it appropriately. That’s why preparing for your U.S. visa interview is so important! The visa interview is your opportunity to explain and share what the Visa Officer doesn’t see on paper, dispel their assumptions, present your situation, and showcase yourself as an applicant.