I understand the BR crowd favor small primers over large ... and among the small, prefer “standard” over magnum. I suspect if they felt a more robust flame produced better results, that is what would be showing up in the winners circles?
IMHO, small primers are just the flavor of the day that's in vogue.
I've seen these things come and go. I will admit, small primers have stuck around longer than most.
As for the smaller holes mentioned by Ganderite. I became a bit anal about such things many moons back. I went so far as to use an end mill ground to size to increase the primer pocket depth, then increase the size of the flash hole and press in a plate with two small holes the same size as in the Berdan primed cases to see if it made any difference in accuracy and velocity.
The rifle used as a test bed was a custom built HBR rifle by Noby Uno, chambered in 308Win. All of the loads were tested over an Oehler chronograph.
I have to say, NADA. Not even a little bit. The average velocities were identical and so were the groups, when compared to the same results from the same cases, before and after alteration.
The other experiment I did, nothing exceptional or new, was to try different size flash holes, which were sized to double the volume of flame from the primer, but still from the center. With Win760 I started getting pressure signs very early and accuracy was very inconsistent. BR 2 primers were used for all of the tests.
I had some RWS cases with flash holes that allowed about 3/4 the volume of flame of standard primers. This time, no pressure signs, very consistent accuracy, with velocities that were slightly lower than those cases with standard flash holes.
One thing about HBR, most shooters build their loads a lot hotter than most manuals will suggest as maximum. This is because the variables are mostly eliminated by very tight tolerances and higher operating pressures are still relatively safe. Consistency is everything and the more variables that can be eliminated the better the rifle will shoot, as long as the shooter does their part and the rifle is accurate in the first place.
Usually the barrels on these rifles are changed out around 1500 round count, sometimes less, depending on the cartridge being used.
I've seen match shooters experimenting with small primers, large primers in standard and magnum types. I knew one fellow that brought in Berdan brass and primers from Finland, because that's what he used there and swore by. He was one of the best offhand shooters I've ever had the privilege to observe.
The only real difference I can see between BR primers and other grades is that the BR primers are hotter than standard primers but the biggest thing is that they are predictably consistent between lots.