My AUD 0.02; having studied both, it's clear to me that PI should theoretically win hands down in a blow-for-blow comparison, if all you do is astrophotography.
The reason for that is simple; PI contains algorithms and features that are not available in PS. They are specific to astrophotography, low light situations and teasing out very faint signals.
It's true that most (but certainly not all) PI features can be accomplished in PS through means of combining multiple operations in actions (or buying add-on plug-ins, which strictly speaking, aren't really part of PhotoShop anymore).
PhotoShop is a tank; expensive, but it will help you traverse most types of terrain you will ever encounter.
PI is a Holden Commodore; cheaper, yet much more capable than a tank, if its main use is strictly city driving and the occasional highway.
Ivo's law: if a program allows you to change every individual pixel to any value within the image's dynamic range, then per definition any result can be achieved.
Both PI and PS satisfy Ivo's law
