Here is a good disscussion on it:
Hottest Rifle Primer - Primers, powders, bullets and brass - Metallic cartridge reloading - The Handloaders Bench
There is a linked test showing flash from various primers.
But I've seen other pressure testing where no real world affect prediction could be made with ANY particular primer across the gamut of cartridge capacities & powders. In fact in some cases magnum primers reduce pressure/velocities. So IMO, it is trial & error, regardless of what a vendor says.
I can say that every gun of mine preferred a particular primer with it's best load. That is, one primer for some unknown reason produces better results than all others, -given all the other components in a load(brass, bullet, powder, seating depth, temps, neck tension, etc). Both primer changes alone, or load adjusted for same velocity with primer changes, still resulted in one better than the others.
Another cartridge, another load, different preferred primer brand/type for some reason...
So I keep most on hand for testing.
It is so abstract.
I've spent the last month testing one primer at different firing pin strike speeds, pin penetration depths, spring forces, and seating crushes. With the test gun I could repeatedly vary MOA of grouping from +1 to -1/4(from a 1/2moa standard) with these adjustments. One primer type though..
Now I need to do it with several primer types, and every action of mine, to try and actually learn something!!