Both schools have a great reputation, however Stanford is clearly superior. Berkeley is, at the end of the day, a public school, and so it’s lumped together with other top public schools like UT Austin or U Mich. Stanford, on the other hand, is a globally recognized private university and more often compared to MIT
In the limited context of a Physics PhD, to people within the physics community, the reputations are essentially identical, and also essentially identical to MIT (though that may be different between the asker's specific subfield, which I am not super familiar with).
Outside of the physics community, there may indeed be some differences in reputation, though I'd expect them to be small, since anybody hiring physics PhD's will have a rough knowledge of Berkeley's excellent reputation in physics. Sure, in other fields (or for undergrad), the reputations may not be equivalent. NB: I'm Stanford undergrad, MIT physics PhD, so I have no personal reason to hype up Berkeley (the opposite bias, in fact...).
> Berkeley is, at the end of the day, a public school, and so it’s lumped together with other top public schools like UT Austin or U Mich. Stanford, on the other hand, is a globally recognized private university and more often compared to MIT
Some data: Last I knew, Times Higher Education surveyed published tenured professors worldwide about the best schools in their field. I think it's probably the best and mabye only good data.
Every year, six schools have been head and shoulders above the rest overall (in random order): Harvard, MIT, Oxford, Cambridge, Stanford, and Berkeley.
People in the bay hold Berkeley in a much higher regard than anywhere else in the country. If you go to Austin people will compare Berkeley to UT Austin, but if you go to Stanford they will regard your school to a higher degree.
I think OP should go with the better PI, however suggestion Stanford and Berkeley have the same level of prestige seems wrong to me
prestige among who? As a physicist, I couldn't care less what my school's prestige was amongst those outside of the physics community. Maybe you want to go work for a hedge fund, where Berkeley is also respected. Maybe it's worse to McKinsey? I don't know. Know your audience.
