This is a hard question to answer. From the way you wrote it I believe you don't actually mean Harvard vs CMU right ?
First of all I believe the schools are not that far away from each other. I happen to have 2 friends (one in mathematics and one in physics) who were in a similar situation.
One declined MIT and went to UBC (but this was because there was a Professor who was leading the field, so it is not because of competetion), I haven't seen him regretting this decision.
The other one got admitted from Cornell physics but decided to go to another country to pursue PhD degree. It is interesting because he also did not regret his decision and was quite happy.
Since you have not given the true names for the Universities this is all I can say.
Congrats on the great admits , hope you make the right decision for yourself.
Legendre wrote:Scenario: Got admitted to a top tier school (e.g. Harvard). Reject the top tier to go to a "lower tier school" that is still very good. E.g. Northwestern or Carnegie Mellon.
Assumption: Both schools have a solid department in the applicant's research area.
Is it ever wise to do this because the top tier school might be "too competitive"? I know an applicant who did this because he doesn't want too much pressure in a competitive environment like a top 10 program.
I might end up in a similar situation too. Having to choose to go to a very good school with nice people and is a nice place to live but not so well regarded, VS going for one of my top/dream choice but not so nice place to live and is likely to be crazy competitive.