Primers are the subject more anecdotal "statistics" than probably any other element of reloading. Based on my exerience and what I've read in sturctured trials, the force of the primer flame varies considerably by brand, primarilly because different compounds are involved. So much so that the flame of a standard primer of one brand may be hotter than that of a magnum primer in another brand. Other factors, like the pressure produced by the powder and set-back, the uniformity and design of the bullet itself, case uniformity and cartridge concentricity all have a greater affect on accuracy than primers. And when a magnum primer is "recmmended" with a prticular the powder involved not just the size of the case but the ambient temperature under which the load will be used.
Type of primer can make a difference. For example, I seemingly get better accuracy using a mild-flamed (pistol) primer loading my Hornet than small rifle primers.Probably because the force of the primer may not blow the bullet out of the case before the Lil Gun powder fully ignites. But then, it could be becasue I started crimping thelittle buggers after I switched to pistol primers. (See, that's how anecdotal 'spit' happens!).
Primar thickness does vary between brands. I learned that when a gun with a defective short firing pin failed to ingnite one brand and not another seated with the same force. According to one article some primers are less stable (allegedly Federal) because of the compounds used and are more likely to go off while seating if too much pressure is applied.
All in all I find that brand of primer makes little difference as long as the same brand is used for a particular work-up. Apparently, the intensity of the flame changes the pressure produced by that particular powder burn but that's a function of powder amount used with that particular primer rather than primer per se. Will I convice someone that CCI's are better than his Winchesters? About as likely as convincing someone who drives a Ford to switch to Chevy.