This is kind of a stupid thread.
* No, your undergrad school doesn't make a big difference. We have people from Harvard, and we have people from No-Name Univ., located in Nowhere, USA.
No matter where you are, if you work hard, do well on the MCAT, and develop yourself as a person, you will be noticed in the application process. Your undergrad school may or may not add something - but in any case, the reputation of your undergrad school is easily overshadowed by YOUR personal achievements.
* OP - the probability that you will STAY a pre-med is fairly low. You may hate o. chem and fail the course. You may realize that, actually, you dislike sick people. (It happens.) After three years of undergrad, the idea of an additional 4 years of school, and 3-7 years of training may make you want to puke. Banking on the fact that you'll want to be a doctor 4 years from now isn't such a wise choice.
Go to the school that you think will help you thrive as a PERSON, and not just as a "pre-med." Both Penn and Princeton have excellent reputations, and I have met med students/residents/attendings from both.
Neither one will "hold you back" when it comes to med school apps.
To a med school admissions committee, Penn basically = Princeton (the difference in "reputation" is pretty tiny - after all, we're not arguing about Princeton vs. your local community college here! For all you people arguing about the "reputation" of Penn vs the "reputation" of Princeton - you need to get a little perspective here.)
So, figure out which one appeals to you more as a student. Then go there. It's a fairly simple answer.