The only real difference I've ever noticed was when people used hard cupped sr primers in their 9mm semi-autos with mid-level loads. They tended to get circular erosion rings in the face of their slides from the hard primers not sealing the primer pockets with the mild loads and flame cutting the circle in the face of the slides.

I tend to use the 9mm's as a dumping ground for any/all old or cheap primers when I make blammo/range ammo for them. Bit I do keep the loads on the higher/hotter side. Old sp mag primers, sr primers, sp primers, they all go bang in the 9mm's.