Use magnum small rifle primers when loading to 5.56 pressures.
Winchester small standard rifle primers and CCI 400's are considerably thinner than magnum primers.
http://www.jamescalhoon.com/primers_and_pressure.php
All LARGE rifle primers are the same thicknes (standard or magnum).
There are two types of slam-fires:
In-battery slam fires.
Out-of-battery slam fires.
The out-of-battery slam fires will ruin your day. Very hard to diagnose after the fact unless it turns up a broken or frozen firing pin. Most likely explanation for an out-of-battery slam-fire is a high primer.
Chances of out-of-battery slam fire can be greatly reduced by using caution during single-round loading. Don't just toss the round into the chamber, and trip the bolt with full force, allowing the bolt to slam full-force against a round in the chamber. With the M14, snap the round into the magazine, and let the bolt strip the round from the mag. With the Garand, keep the edge of your hand aganst the op-rod while CAREFULLY depressing the follower. Ride the bolt forward for about half the range of travel, and only then release the bolt to allow it to fully seat the round and lock.
As already noted, the best explanation for the in-battery slam fire is the force of the bolt slamming causing the (probably modified) trigger to release due to the shock of the bolt slamming. Here again, the chances of shocking the trigger to release on an M14 or M1 can be minimized by utilizing the single-round loading procedure I stated.
We hear about the occasional slam-fire with AR15 guns. With so many of these guns on the ranges, there are bound to be a few incidents. That said, there seem to be, proportionally, far fewer slam-fires from single round loading with AR15's. Not sure why that is, but it is my observation that such is the case. I have no advice for carefully loading single rounds in the AR15. You can load singles into the mag, and pull the mag on each shot. People just aren't doing that, and it does not seem to be a problem of any magnitude.