As an MBA from a long time ago, I think it is important to point out that an MBA has the most impact on your career trajectory within the first five years. In my own cohort, some people leverage their MBA to get on fast tracks, some people chose careers that they did not stick with. If you recently got an MBA a lot of people will hire you for your pedigree and education. If you got an MBA ten years ago, people care about your most recent job experience. Employers will always screen for college graduates, but once you get to a certain point in your career they care less about an MBA and more about experience.
the difference is that it's pretty easy to tell a good b school (lots of objective rankings). at an early stage, it's really tough to tell a good startup- as a candidate you are at a significant disadvantage in choosing a startup employer due to the lack of available information. not saying one is better than the other, but that making that choice is far more difficult than the couple of sentences you mentioned.
On the other hand startups pay you money, B schools cost you money. With the delta easially being 300+k. So, you can take a fair amount of risk and still have the startup being a better bet.
If you choose a good start up, then the start up (and payout) will most likely be much more valuable 10-20 years down the line.