Just an anecdote: My in-laws were tenured profs at Central. My youngest SIL got both her undergrad and MBA at Central and is now CIO at a place everyone here would recognize. The rest of the sibs went to U-M and none of them have landed quite as high as she has. I think it’s utterly ridiculous to worry about long-term career prospects between two good universities when it is impossible to predict that outcome for any individual. The school is not the determining factor. Save your money and enjoy the lovely town of Mount Pleasant.