I've definitely experienced both instructors, I've also experienced the instructors that are required to teach and you know they'd rather be doing their research. From what I've come to learn from my friends in medical school, a lot of these instructors spend their time reading off PowerPoint, rambling, and telling you how awesome their research is.
Plus at these great institutions that you speak of, you'll get instructors that are top in their field, but they won't teach you, they'll talk at you. This is what I've learned in my short life here on this earth, even interviewing at a Top 10 many of the students reiterated the same thought. They said how awesome it was to have this world renowned 'X' teaching but really all they would do was ramble through the power points, talk about their research, or even be incredibly specific about things you don't even need to know to do well in that course. You get me now?
EDIT: but yes prestige matters, just not for the #1 reason you consider important