Your counselor is clueless. Stop listening to his/her advice. Stop fixating on acceptance rates and what happens if you decide to transfer to another school. Btw, Michigan’s acceptance rate is currently at about 26% for all students, with internationals much lower. Assuming you do well as a freshman, you can easily switch colleges with the exception of Ross and some niche programs.
I have to agree with rjk. Your counselor seems to be lumping Michigan with some public universities that have strict rules regarding the switching of majors. Michigan is fairly pliant when it comes to changing majors, with the exception of a few programs, such as Ross (Business), PPE and Public Affairs. Switching from the College of Engineering to the College of Literature, Science and the Arts (LSA, or Arts and Sciences) is usually automatic, as long as you are a student in good standing (C average). Transferring from the College of Literature, Science and the Arts to the College of Engineering is not as straightforward because of the Engineering prerequisites, but still relatively easy, as long as the student has a B average.
Michigan’s overall acceptance rate at the moment is roughly 25%, although it is significantly lower for international students (approximately 10%, although this figure is unconfirmed).
As for tuition, the figure universities release do not include medical insurance, which is required for international students, and international travel expenses. Those two alone will add $5k to the total cost listed by the universities. In addition, students spend quite a bit on personal expenditures, such as clothes, technology, entertainment, holiday travel etc…
Is Northwestern $10k/year better than Michigan? On an absolute, obviously not. Michigan and Northwestern are peers and offer a similar quality product. But if you can afford both, and Northwestern is a better fit for personal reasons (closer to a huge city, smaller student body, better at your chosen major, more friends on campus, stronger reputation in your country etc…), then the $10k/year would be well spent.