Having one kid at Harvard and one at Yale, I’ve got to say that Yale fosters a spirit of being part of a larger world more than Harvard.
For example, Yale has a world-wide day of service (http://yaledayofservice.org). Harvard does not do anything similar. Yale has master’s teas (http://yaledailynews.com/magazine/2012/04/04/celebrity-masters-teas/). Harvard does nothing similar, although they do invite guest speakers from time to time, but those are usually held in Memorial Hall, which seats about 1,000 students.
If you’re looking for a comparison of each school, I wrote this a couple of years ago. See post # 4: http://talk.collegeconfidential.com/yale-university/1483765-choosing-yale-over-stanford-and-harvard-p1.html.
In addition, also read Marina Keegan’s love letter to Yale: http://yaledailynews.com/crosscampus/2012/05/27/keegan-the-opposite-of-loneliness. No Harvard student I’m aware of has ever written such a love letter to their school.