ucbalumnus, the SES distribution probably is not much different at Y or P (though perhaps a little), and it does raise issues elsewhere, too.
On the other hand, I think that Harvard culture probably leads to a little more emphasis on “winning” than at other schools. Competing to get into EC groups? I have heard students express frustration that after a long slog of competition, they reach Harvard and find yet more competition. Others could correct this view, if it is a misperception. Also, I think that Harvard students are advised to a slightly greater extent by each other, rather than by the faculty or other experienced advisors (relative to students at Y or P). This could be wrong, too–my sample size is pretty small, but this is what I have seen.