There’s nothing wrong with choosing to put a public school on a PhD application list if one has done his/her homework about subfields of interest beforehand. But the discrepancy between domestic and foreign students’ admissions standards is usually greater at a public school than at a private school. You should know by now that most schools will not accept students they can’t fund. If you earned a fellowship, or otherwise secured outside funding, yes, that might reduce the pressure on the department, but that doesn’t change the fact that even so, foreign admissions standards are higher even for those on outside funding. There is a reason for that: the tuition waivers that come attached to the funding (whether TA or RA).
Speaking of which, the cost of granting a tuition waiver to a student depends on the student’s state residency, because of the cost of the tuition being waived. How much do the cost of the tuition waivers explain the discrepancy in standards required from domestics vs. internationals is left to debate, but tuition waivers do play a role. And this would cause even out-of-state domestic students to be held to a higher standard than in-state students, but with no further disadvantage beyond that of state residency from that source. So here are two cases I’ve heard about at US public schools:
- University of California system. This is a system-wide issue, but UCs in general require out-of-state domestic PhD students to establish California residency within one year of the date of first enrollment, otherwise they will have to pay the difference between in-state and out-of-state themselves. Since establishing California residency is something an international student just cannot do on a F-1 visa, internationals cost more money on the long run. Also UC Santa Barbara is a campus known to have reduced the quotas on international students, to the point that the number of international admits can be counted on one hand for the 2014 cycle, and all other UC campuses are likely to follow suit in the near future, invoking that much of the research conducted at UCs is state-funded (NSF, state appropriations, etc.) and that they wish to keep the funds in the country.
- University of North Carolina system. By state law, all public schools in the state of North Carolina (other than UNC School of the Arts, NC A&T engineering and MD/PhD programs, the latter because of NIH regulations) must enroll at most 18% of out-of-state students, internationals included. EDIT: UNC campuses enforce the 18% cap at the campus-wide level, leaving some leeway to enroll more out-of-state PhD students if the need arose.
On the other hand, private schools usually charge the same tuition regardless of the student’s origin, in which case the discrepancy is not explained by the cost of funding a student, but simply by the sheer talent to be found in the applicant pool.