Not for precision rifle. Board member Hummer70, who was an Aberdeen Proving Grounds Small Arms Test Director said he did a lot of testing of primers. He found every danged one of them produced more accurate ammunition in some guns and with some powders than the others did. Unfortunately, this means more testing for the precision rifle shooter, but it's doable.
For handguns, though, I think you are right that it doesn't matter a lot whose primers you are using, as long as the gun fires them consistently.