Your greatest competition will be applicants with similar profiles. In other words if you're a consultant, consultants are your greatest competition. If you're an engineer, engineers are your greatest competition and so on.
With regard to nationality, schools also want a healthy representation of international and domestic students in their classes so it definitely is a factor, although not nearly to the degree that a lot of applicants suspect.
One question I get a lot is: How can so many South / East Asian applicants with super GMAT scores (750+) get rejected from top programs? The simple answer is that many focus way too much on the GMAT and completely miss the boat on the other application components.