I can say exactly what happens with 38 Special, 4.2 grains of Winchester 231, and 158 grain LSWC. I accidentally loaded some with CCI 550s instead of 500s, and ran them over the chrono to see what happened. How this applies to anything else is anyone's guess.
S&W 442, 1.875" barrel:
CCI 500 primer Average speed 744 Standard deviation 13 Extreme spread 33
CCI 550 primer Average speed 731 Standard deviation 20 Extreme spread 51
S&W 586, 6" barrel:
CCI 500 primer Average speed 812 Standard deviation 12 Extreme spread 32
CCI 550 primer Average speed 795 Standard deviation 13 Extreme spread 34
I'm assuming same day. Just spitballing, but maybe the magnum primer "popped the cork", i.e. moved the bullet slightly and sooner in the burn sequence, effectively increasing case capacity slightly for the powder burn. Or, perhaps there is some way that a magnum primer versus standard could have some interplay with position sensitivity with a non-case-filling powder.
Anyway, I once compared WSP's to Federal SPM's in 357 magnum. It's just what I had. There was an average increase of 0.7% with the magnum primers, which in those loads meant only about 0.4 standard deviations. I was unimpressed.