I want to second some stuff that ironey mentioned. While I don't start school until this fall, I've learned some stuff in the application process.
First, know that p/f is not p/f in many schools. When I visited NYU for example, they told me that its so relaxed because the first two years are pass/fail and in the clinical years, everyone gets an A, A-, or B+. I went on and asked them how the school can distinguish between students when they apply to residency, and also how they go about awarding an honor such as AOA. With a little pressing, everyone pretty much admitted to me that while your transcript is P/F, the Dean's office knows who the top students are. Basically, if you want a competitive residency, don't fool yourself into thinking that your 71 is as good as someone else's 96 just because your transcripts both say "pass." That said, NYU is still a pretty chilled out place.
At Einstein however, I ran into a similar situation where they also have p/f for the first 2 years. I pressed them with the same question, but they stuck to their guns. I even know someone who did average in his first 2 years, but recieved honors on 5 out of 6 rotations and got AOA. So, my advice is to ask questions of each school and don't let them feed you BS answers. Find out the reality as best as you can. It most likely will come from students and not from the Adcom.
If you are really looking for no competition, I suggest looking into a school such as Yale, where p/f is really pass/fail and no rankings are assigned because there is no AOA. Obviously, not eveyone can go to Yale, and most schools don't go to the extreme of the Yale system, but there are a bunch out there who don't do AOA.
Personally, I need some kind of motivation to push myself to work harder. Many people are motivated enough to study for 10 hours a day, even for a pass. While I don't plan on being a gunner, I think I need something to work towards instead of just trying to "get by," even if getting by in med school still means putting in countless hours of work. Other people would rather not have to be anxious about how they fall in the curve, and therefore opt for pass/fail. (ie- When I told a friend at Yale that I was also interviewing at Hopkins, he told me that if I would even consider Hopkins, there is no way I should go to Yale. In the end, neither school wanted me, but the story proves a point.) You need to ask yourself what you think you need to succeed.
On a final note, look out for pass/fail/honors. These systems are as good (or bad) as grades in my mind. Honors=A, Pass=B. Its silly that they think they can mask it, but they try.