I think, given that you can afford Michigan and that it’s his first choice, it’s worth the extra $80,000. And I say that as a Bama parent whose kid happily turned down the more prestigious degree from our state flagship and never looked back.
The STEM Path to MBA program at Bama is pretty cool and gives students some real business exposure (and for the student with enough AP credits, it frequently can be completed in four years and would likely be a piece of cake for the OP’s son with the NMF package, which includes a fifth year). Personally, though, I don’t see a whole lot of extra value in the MBA earned because, with no prior work experience, I’m just doubtful many employers will be all that impressed by it. For someone like the OP’s son, given his aspirations, it makes more sense to me to shoot for an elite MBA program after working for a few years.
If your son visited Bama and got a chance to consider all that’s being offered to him and still feels Michigan is the better value, I’d let him make the choice, knowing that any postgraduate education very well may be on his own dime.