anachronism has touched on it, an I'll add some, it takes a full chapter to explain primers.
It's about the surface area of the powder in the case, the size of the case and the amount of powder in the case.
That's why load manuals can be a bit deceiving, they chose a primer for the load and use it with all the powders tested so they only change one variable, powder type and charge for us average guys to review.
Magnum primers are
not "hotter" than standard primers. The make up of the chemicals used in magnum primers has a higher metal content like aluminum that will throw the burning primer charge deeper or further into the case to ignite a powder along the full length of the case instead of from just the end.
The powder burn rate and surface area now comes into play. While the pressure developed can/will be within safe limits with either primer, powder burned slowly (ignited from the end) will
spike at a different time in the sequance than the same powder ignited along it's full length in the case.
So this is why a primer choice will change the entire load characteristics and accuracy, the powder charge might need to be different with a primer choice. The combination of powder, primer, case size and shape, and bullet weight all factor into when is the best pressure spike in the firing sequance.
Here's some really good reading and study of primer stuff by German Salazar, ya gotta go back to his "Articals Index" to link to small primers;
http://riflemansjournal.blogspot.com/2009/06/primers-large-rifle-primer-study.html I gotta add that accuracy can be found with most primer/powder combinations, people do it all the time. I know some that will use only Mag primers just to simplify purchase issues, others start with a given primer for whatever reason and simply consider those the best because they work for them.
I'm not one to worry too much about primer choice, but I have found a differance in the application to different guns. Tried Rem 9 1/2 in a buddies 308 AR, and found Win Mags to be the ticket for that gun. Then theres the size and hardness of the cup,,,