Let me share my perspective as a South American who lived in Europe and now is in an American School.
I agree that if you just look at the raw numbers, European schools may seem more diverse than US schools; nevertheless, it is hard to compare diversity. My experience is that US schools have fewer non US citizens, but, this doesn´t mean less diversity. The USA is a big country with people from several diferent regtions of the world living there, I had in my first year classes with americans who are from families that migrated from China, India, Pakistan, Iran, Brazil, Argentina, Nigeria, and Europe in general - just to ilustrate some countries that popped up in my mind. Even though they are somehow "americanized", one can´t say that they are all equal. In terms of language, it is true that one may have less exposure to different languages, but I feel that, at least at Booth, there are enough people so that you can somehow have a decent amount of exposure to different cultures. I have been talking more than I wanted in Portugues with my Brazilian and Portugues fellows, I've been practicing Spanish with people from Spain and South America, and "trying" to learn something of German with the guys from Germany, Switzerland and the Polish guys who speak German.
I agree that it is easier to go from a US school to Europe than the other way around, but it is easy to go to UK. Remember that to work in most countries in Europe one will either have to have an European Passport or will go through a painful process of getting a Visa, believe me that Visa in Europe is a Pain in the neck, and the company must truly help you through the proces - it took more than one year for me to get a Visa when I worked there.
One thing that I am somehow "disappointed" is that in my opinion US schools are too US centric in terms of cases and examples - and I checked with friends at other US schools and they told me that they have the same approach. I understand why, but I´d like to have a more "global approach". At this aspect, I believe that European and perhaps Asian schools are better. That said, I had a course called International Financial Policy, in which we discussed things such as the US Budget Deficit, the Chinese economy, the Brazilian and Argentinian Central Banks, Sovereign Wealth funds, etc.
40% of students were born outside the US at my class (Booth 2010) are, and the number of women is aprox the same (if I remember correctly it is 38%).
Rhyme´s guide to interviewing