I have a bud, worked as an Army Gaging and Calibration Specialist at an Army Ammunition plant. He is interested in shooting so he asked questions. All Army Ammunition plants are run by the same contractors who produce your ammunition. In fact, once the military orders are met, they are allowed to use the facility to produce ammunition under their brand name to sell.
Anyway, primer mix is a mix of chemicals. The standard primer mix for military primers is the FA 956 mix, developed in the 1950's as a joint project between the Government and Industry.
PATR 2700 Encyclopedia of Explosives Vol 8 gives the composition
FA 956
Lead Styphanate 37.7 +/- 5%
Tetracene 4.0 +/- 1%
Barium Nitrate 32.0 +/- 5%
Antimony Sulfide 15.0 +/- 2%
Aluminum Powder 7.0 +/- 1%
PETN 5.0 +/- 1%
Gum Arabic 0.2%
There are plenty of primer compositions for there are many applications for primers other than small arms. This is a list of military priming mixtures, FA 70 is the old corrosive primer, I was able to identify PA101 as a fuse primer composition. All of the compositions to the right of FA90 are more sensitive than rifle primer compositions, so these are probably used on a variety of explosive or propellant devices.
It is very likely that Federal makes a different primer mix than Winchester or CCI for their military primers. The Army has moved over to performance specifications and as long as the product meets sensitivity, temperature, pressure requirements, they don't care anymore what is in the product. This is probably true for primers. What you will find is that each manufacturer provides the Government a "Mil Spec" primer, but only CCI offers their Mil Spec primers to the public.
George Frost, in his book,
Making Ammunition shows a whole bunch of different variations of the FA956 mix as used by the various commercial manufacturers for the same applications.
Notice that the constituents used all have tolerances, so each batch of primer mix will be a little different based on mix percentages and purity of the constituents. And, as my friend told me, the most consistent primer mix du jour is not predictable. Employees are rewarded for making the most consistent primer mix so they have a financial incentive, and it is probable that the prize rotates around a couple of the makers. But it is not predictable who gets the prize of the day.
This is a great article on primers:
Mysteries And Misconceptions Of The All-Important Primer http://www.shootingtimes.com/2011/01/04/ammunition_st_mamotaip_200909/ I recall reading that CCI Benchrest primers are made under tighter controls, they actually weigh the individual primers at the end. I do not recommend Bench Rest primers for semi auto rifles as several primer companies have told callers that the bench rest cups are thinner and the mix is more sensitive than military primer mix. This will increase the chance of a slamfire. I cannot find the post but one shooter of a real full auto Army M14 loaded new cases with bench rest primers. Shooting his M14 full auto, he had the rifle fire out of battery. Luckily the receiver heel was not knocked off or he would have been out $25,000 or more.
Now will bench rest primers make your groups smaller? Maybe for the best shooters but it will be something hard to determine with any exactness. Accuracy affects due to primers are in the noise level compared to bullets, powder charge, cases. And all of these have a smaller affect on accuracy than the skill of the shooter. Marksmanship is a skill, good equipment and good ammunition cannot compensate for poor shooting skills.
I do have F Class friends who experiment with primers, many of them are using CCI Bench rest primers, so they must be good. I have shot many cleans on the two MOA targets with standard primers, if the shot is not in the ten ring it was not due to primers!