Measuring change is going to be highly specific to powder, charge, brass, and bullet. You may have slight velocity or ES/SD changes with a primer change, or even a slight accuracy edge. It's related to consistency and ignition of the priming compound and powder, some (rem 7 1/2) create quite the flame, while others (FGM205) are significantly milder. I wouldn't worry too much about it unless moving from a normal to a magnum primer.
And if that answer doesn't suit you, head to a benchrest forum and go down the rabbit hole. German Salazar did a pretty good writeup on primer differences, if you can find it.
I've noticed some differences between primers, but it's never enough to positively sway me from one brand to another, although i tend to stick to match primers (because ego, not because demonstrably better). I'm currently working through some FGMs, with a case of BR-2/4s in reserve.