from the Speer reloading manual.
Magnum Primers
Magnum primers contain a greater amount and/or slightly different explosive mix than is used in standard primers. On ignition, magnum primers give longer burning, hotter flames. Their use is recommended for (1) any ammunition that will be used at or below zero degrees F., (2) with most Ball powders and (3) with slow burning rifle powders like MRP and IMR 4831 in very large cases. Magnum pistol primers often will give more uniform velocities in magnum handgun cartridges loaded with large charges or slow powders like 296, 2400 and H-110. Magnum primers may be used with faster burning or easy-to-ignite powders, but normally there will be no advantage in doing so. As when changing other components, it is advisable to reduce powder charge weights on initial loading with magnum primers.
Magnum primers tend to have a thicker cup material also.
When I was hunting or target shooting back in MN there were times that extremely low temps (-30) that I could hear the firing pin strike before the shell ignited, never a missfire but a slight hang fire with standard primers in larger cases and have pretty much gone to Magnums for all my hunting loads and high intensity loads. I use standard SR primers in the 22H and 218 Bee and cast bullet loads and magnum primers for all others.
LR primers I use standard primers with all my rimmed cases 22 Highpower, 6.5x58R, 9.3x72R with stick powders and cast bullet loads in all cases and Magnums for everything else.