<p>It depends on how you want to compare them. In terms of overall prestige and reputation, HYPSMC is the top tier, period. The same tier applies in terms of selectivity. For overall strength across departments, Stanford is virtually unmatched (at least at the graduate level). I’ve seen at least one ranking where Stanford is ranked 1st. The methodology was based on the number of highly ranked departments, with more weight given to those that are ranked in the top five, less to the top ten, etc. However, in terms of quality of undergraduate education, it’s hard to tell and difficult to measure. USNews seems to think that Penn is slightly better. Many people seem to think that Penn’s rank is inflated. I don’t think that it’s quite at the level of HYPS yet. Nevertheless, Penn’s an amazing school and I marvel at how much it’s improved over the past few decades. It’s certainly comparable to Stanford (practically all the top 25 schools provide comparable educations), but to claim that it’s better will raise a few eyebrows.</p>