Military ammunition is all made with magnum primers or their equivalent. This is to ensure consistent ignition in extremely low temperatures. Therefore, you may conclude that there are few situations in which they may not be substituted, provided you work the load back up.
There is no generic relationship between magnum primers and pressure change. How primers are compounded changes over time. Some magnum primers have been made by simply increasing the size of the pellets, but I believe most are done by leaving the net level of the sensitizing lead styphnate alone while increasing the portion of fuel compound to make more gas. This lowers the brissance of the mix from that of its standard counterpart. The primer companies have changed these mixtures and the thickness of the primer cups over the years, and they don't announce these alterations with any great fanfare. So, you need to be aware that each new lot of primers you get has a chance of being different from the last.
QuickLOAD's author, in its manual, points out that the result of the above is that while magnum primers usually raise start pressures, there are situations in which they can actually lower them, as well. I see that most often short pistol cases firing lead bullets, because the magnum primer unseats the bullet before the powder burn gets very far. That increases the volume the powder is burning it, lowering pressure. It's not a very consistent effect, so if using a magnum primer makes your muzzle velocity ES higher, that's a sign you should avoid the magnum primer and go back to the standard type and get your velocity gain by raising the powder charge instead.
Watch out for the velocity of an old load to change. There is no exact relationship, load-to-load, but pressure can increase by more than the fourth power (square of the square) of the change in velocity if the powder charge is unchanged. So back loads down and work them back up. There is no free lunch in ballistics.
There is a good article on primers by a former CCI employee,
here.