Another international student considering Cornell here. If by job prospect, you mean academia, I have not paid much attention to it. But if you include industry, it seems that alumni from the labs I'm interested in don't have a problem in getting into competitive companies - be it pharma, material, etc. I'm in organic though, so a lot of us end up in industry.
The weight of the name is probably slightly less, but most professors now, even from Caltech and such, did post-docs anyway. So, you can always buff up your resume that way. Your PI and PhD projects will be the other big factors too.