Assuming you're paying full in-state tuition for Michigan State University, your total cost for all four years would be in the neighborhood of $100,000. The question of whether the school is enough of an improvement over Eastern Michigan to warrant this price tag is a tough one to answer. I think it depends on your financial situation, what your areas of academic interest are, and how much you actually like each of these schools.
First off, you say you will have to take out loans to pay for tuition. Do you think you may be eligible for financial aid to lower your tuition costs? Will your parents help you out at all? Investigate your options a little more so that you know exactly how much more Michigan State will cost compared to Eastern Michigan. Try contacting the financial aid office at Michigan State, and ask them about their take on your situation. You may have to pay less than you think.
Secondly, I think you should consider your academic interests and the relative strengths of the programs at each school. If you're planning on going into a STEM field, it might be worth it to go to a larger, more well-resourced school like Michigan State where you'll have access to better research opportunities and potential paths to graduate school. If you want to major in the humanities, it might make less of a difference which school you attend. I'd encourage you to investigate the specific programs that interest you at each school and see what their relative strengths are.
Lastly, I'd advise you to visit these schools if possible and see how you feel when you're there. If you find that the campus culture at either one is not what you're looking for, you might have a pretty easy decision to make. You shouldn't attend a school if you don't like the environment or the living situations offered to you.
I lean towards advising you to go to Michigan State because, as you point out, it's a significantly better school academically, and has historically led to better career outcomes than Eastern Michigan. However, there's certainly something to be said for being debt-free, so you should make a final decision based on further investigation into your financial situation and ultimate goals for your college experience.