I'm a grad student in the chemistry dept at UC Berkeley (arguably the best school in the world for my field). My department is mostly American; it's much harder to get in as an international student.
For public schools, US citizens are cheaper to pay for (since, in the sciences at least, the dept/your advisor pays your tuition. US citizens can get resident tuition, while international students can't). This is one of the major reasons that UC Berkeley has so many American students, followed by the top of the top among international students.
Undergraduate research is also really important in the admission process in Berkeley's chem dept. It's assumed that you have done research before coming here, and a lot of international schools don't push their undergraduates toward research experience. So again, US students have an advantage in the admissions process.
Anyway, this probably varies from school to school. Public/private is one divide to consider. Top 5/not top 5 is another.