You have an interesting question, and a very nice-to-have problem. Congratulations on getting the two offers.
Any person after MBA from any top school joins as an Associate irrespective of the number of years experience they have prior to their MBA. If you have an offer with McKinsey as an ‘Engagement Manager’before an MBA, it is really brilliant. It also shows you have some expertise that McKinsey values. Morevoer, McKinsey brand is very strong. Remember, an MBA from a top school is a long term investment. You can always join McKinsey sometime in the future. But, a business school is not easily possible because I think age will be not on your side. If I were you, I would go to the business school.
Alternative is to negotiate with your school to get best of both worlds. Tell them you have an offer with McKinsey and request them to defer to the admission by one year. It is always good to get McKinsey on your resume for long term results.