Harvard has great PR, but it's a quite good school. I think most professors if asked to list the top 5 American universities in no particular order would probably say Harvard, Princeton, Yale, Chicago, and either Stanford or Berkeley. This ranking is rather odd, I certainly don't think very many would put MIT, Cal Tect(which has like 6 majors), and Stanford all above those other schools.
It's difficult to answer the second part of that question. It's undeniably a better education. You have better faculty, and classes not taught by at lest fellows are essentially unheard of, in significantly smaller classes, in my undergrad I only had 2 classes with more than 12 students. They are also generally oriented around seminars and not lectures. I vastly prefer the former, but more shy students generally hate having to talk.
They are also generally extremely affordable compared to schools lower down the ranking but still high seeing as the match all demonstrated need.
The most obvious downside is that your social scene is dominated by the kind of person who goes to a high end university. On the whole this is not a particularly nice or fun group of people. Most of the good schools are very similar in character. Chicago is the standout one, but its culture is just as bad but just in a different way.