As far as I know if you attend a US high school your application will be read by the regional officer who has certain knowledge about the education system there, so you’ll be compared to other US applicants from that region. It sounds a bit illogical if the officer who reads your file is the one who specializes in Chinese school system and has no idea how different the schools in New Jersey and New Mexico are, how competitive the students, which activities are offerred, etc. The applicant who has 8 years experience with horse riding for ex would probably stand out in the NJ pile and the Chinese student pile and not the NM pile…
I think you’ll compete with other internationals only at the committee and when finaid, etc. are taken into account. The admission officers will try to understand you as best as they can first (which is the purpose of the regional reading) before trying to compare you with somebody else (well, I hope)
Nonetheless I think it also depends on each school’s way of processing materials. The one which has large applicant pool will be more likely to read files according to high school locations.