The article Dufus linked to contains good examples of the stuff that drives shooters crazy trying to make sense of. Note the CCI 250 magnum primer produced less velocity in his test than the CCI 200. Note the Remington 9½ producing the worst MV spread but the best accuracy.
I've heard at least three different benchrest shooters comment that different powders and chamberings just turn out to like different primers best. Variation in flame heat, brissance, gas volume, metal sparks tossed, etc., all seem to favor some powders over others. Unfortunately, this means testing different primers becomes part of any truly optimal load tuning.
The good news is that what affects benchrest groups printing sub-moa often has little visible impact on groups 1 moa and up. Notice the velocity difference in the article Dufus linked to is only 35 fps average from high to low, about 1.3%, and accuracy varied from 0.42 to 0.7 in diameter. Lots of shooters would be happy with either group size for a lot of purposes.
Small primers are another matter. They seem to have more influence over the powder, probably just because the cases they are used in are normally smaller than those for LRP's. In 2006, Charles Petty had an article in Handloader that showed about 150 fps difference (about 5%) for some 223 Remington loads (about 3150-3300 fps) for a 55 grain V-max. That's more than enough difference to drift you in and out of load sweet spots, and, with the powder he was using (24 grains of RL10X in 24" tube, IIRC), it represented about 17.5% difference in peak pressure. So it's something to keep an eye on in the SRP fired chamberings.