Back to the original questions. There are compositional differences existing among priming compositions depending upon manufacturer and primer type. But there is very little difference in ballistic performance among the same types of primers from different manufacturers, as things such as impact energy required for primer ignition are pretty well standardized within the industry. The whole business about Winchester having a soft primer and CCI having a hard primer, etc., is total fiction, promoted by those who have no facts to support the assertion, so long as the same types of primers are being compared. Rifle primers typically have heavier cup material to better withstand heavier pressures, and in some cases, such as CCI NATO primers, the primers are designed to require a heavier firing pin blow to prevent slam fires in semi- and full-automatic weapons. Regarding small rifle and small pistol primers, they are dimensionally the same and it's possible to use small rifle primers in small pistol cartridges (but not vice-versa). I have tested this extensively in .38 Special, and have found absolutely no difference in MV or grouping capability. However, a lighter firing pin strike may result in misfires if small rifle primers are used in a specific gun. I have had no problems with the use of small rifle primers in any of my revolvers. Not so with the use of large rifle primers in large pistol primer pockets. There is a dimensional difference, and a large rifle primer, when seated, will not seat flush with the base and will cause headspace problems. The use of a large pistol primer is a rifle case will work, but it is dangerous due to the higher chamber pressures involved in a rifle.
The most extensive treatment of primer technology is to be found in Frost's book "Making Ammunition." However it is currently out of print and copies are hard to find and expensive.