As an undergrad, realistically, the biggest academic difference will likely be the quality of your fellow students, which will be better at Harvard. And that's nothing to scoff at. Professors? Yeah, they might be "better" at Harvard, but the sort of "better" that gets a professor hired at Harvard vs. Michigan is not necessarily relevant to an undergrad. Prestige and perceived quality, absolutely a difference - actual quality of education, in a way that affects a very good student? Much closer, close enough to be reasonably trumped by other factors.
When you talk about "firms that see Harvard grads on the regular" you're really talking about professional grads (and in particular business types and lawyers) - and in that case all that matters is where your MBA / Law Degree came from, not so much where your undergrad degree is from. And you can get into Harvard Law from Michigan (or get rejected from Harvard Law from Harvard).
If you're doing some other sort of grad school (e.g. a STEM field), your individual advising professor matters a lot more for the quality of your education than the actual school you're at.
To be honest, the pro-Ivy, anti-state school bias seems much more pronounced on the East Coast. Out west, they're obviously respected very highly but you don't get near as much of the "we only hire Ivies" attitude.