I'd be interested to know how international experience or language skills are perceived in management consulting in the US. It seems to me (I may be wrong...) that there are relatively more foreigners in banking. I don't know whether it's the difference in nature of the work that favors diverse backgrounds, or is it that banking appear more attractive to foreign talents.
Applying for jobs in consulting internationally is actually very tricky. First, it is important that you have language skills in the country in which you will be recruiting. So if you are looking to join the Tokyo office, you need Japanese language fluency. If applying to Madrid, you need to speak Spanish. If you have this background, be sure to mention this it in your consulting resume and consulting cover letter.
At McKinsey, I found my colleagues were very international in nature. I worked with Germans, Australians, Japanese, and more. However, all of them were transfers. So the German I worked with was hired in Germany, worked in Germany for 2 years before moving to New York.
If your educational and job experience background is one country, say Germany, but you are applying for a job in say France, you may not get a first round interview for the simple reason that the person who happens to be reviewing your resume or CV may not be familiar with the Spanish education system, major employers, etc.. In this case, you are much better off applying to the office where there will be people who can correctly understand and appreciate your background.
In an ideal world, the application reviewer would ask a colleague with a background similar to yours to evaluate your application. In reality, we are busy people and there are plenty of applicants whose backgrounds we do understand without any extra work.
I had one person who could not get a single interview in the country of her choice (which was not her home country). I suggested she apply to the same firms in her home country, and she did very well - and ultimately got an offer from McKinsey.
This advice is not all obvious and reflects the fact that people in these firms are the ones doing applicant evaluations. It's impossible for one person to have the background knowledge to be able to evaluate every application from any part of the world. So its important to figure out who has that background, find them, and make sure your application enters their hands.