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...).
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...).