In math and science, both universities will provide you with excellent opportunities. Michigan has a slight edge, but UNC is no slouch. In Engineering, Michigan has the clear advantage, mainly because UNC does not have a traditional college of Engineering.
I am not sure about UNC, but Michigan does not provide need based financial aid to international students. Since UNC is public, I would assuming they too do not provide financial aid to international students.
I think both schools are excellent, academically and non-academically (social, athletic etc…). You really cannot go wrong with those two universities.