Number 34 Primer with .303 British

[Bruce_in_Oz]

I guess it also depends on your chosen propellant..

US powders like 3031 and 4895 are excellent for driving 150gn bullets from a .303. You can happily ignite those powders with ANY "standard" Large Rifle primer.

I stared reloading Boxer-primed .303 with Remington 9 1/2 primers fifty years ago. Later, I moved to CCI standard Large Rifle primers , partly because, in these parts, they became easier to find than the Remingtons and they seemed to be a little "tougher" in "stiff" hunting loads in .30-06. Thicker cups?

Regardless of the cartridge, the usual caveats apply:

HEADSPACE, Max load warnings, triim length, flash-hole diameter, striker protrusion and radius, striker /striker hole "fit". etc.

If you are loading heavier bullets , eg. 180gn and above, a slower powder is advised. Endless good data in print and on line out there, Powders, primers and bullets come and go over time, so you need to keep current with data..