Other than the issue of who claim the tuition credit, with the tax law change, effective 2018, most students will get the same refund whether they claim themselves or not. The personal exemption has been eliminated and the standard deduction increased.
A full time unmarried student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working (more than half your support must come from earned income). You cannot be supporting yourself on parental support, 529 plans or student loans & grants. It is usually best if the parent claims that credit.
You cannot claim a credit if you are, or can be, claimed as a dependent by someone else.
