I have heard, and read, that Nato ammo is loaded to higher pressures. Compounding this, Nato chambers are cut differently than 223 chambers. In the nato chamber there is a bit of space from the end of the case to the point where the bullet actually bites into the rifling. (Or the other way around!) This lowers pressures a bit, which ALLOWS the Nato ammo to be loaded to higher pressures. When you shoot Nato in a 223 chamber, that freebore is absent, and pressures can spike.
Or so they say. Can't always believe what you read and hear, but that explanation seems to make sense.
One - There is no such thing as a "5.56mm NATO" chamber. There is an M16 chamber, and M249 chamber a C7 chamber, a G36 chamber, etc., etc., even the test barrel used to test military ammunition is not the same as any of the various rifle chambers.
And even among the "M16" family will all the different civilian barrel makers out there, there is a wide variety of chambers all marked "5.56 NATO" on the barrel.
In general, the military chamber have a longer freebore, the cylindrical portion of the bore prior to the start of the rifling. This allows the bullet to get a 'run-and-go' at the rifling reducing the pressure needed to engrave the rifling on the bullet.
TWO - There is no such thing as "NATO pressure". STANAG 4172 specifies that the chamber pressure of standardized ammunition shall not exceed an average pressure of 380 Mpa (55,114 psi) with a average plus three standard deviations of 420 Mpa (60,915 psi). But, US ammunition is not made to STANAG specifications regarding pressure, and judging from pressure tests on various lots of foreign ammunition, few other countries are either.
So, let's look at some available ammunition and their maximum average pressures specified:
M193 (MIL-C-9963) = 55,000 psi
SAAMI (ANSI-SAAMI-2299.4-1992) = 55,000 psi
STANAG 4172 = 55,114 psi
M885 (MIL-DTL-63989) = 58,700 psi.
.223 Remington and M193 Ball are loaded to the same pressures and M855 Ball is slightly higher. Most of the measured pressure difference people see when firing military ammunition in .223 Remington chambers is due the throat differences, not "because military ammunition is loaded hotter".
The often quoted C.I.P. pressure for 5.56mm x 45 of 62,000 psi cannot be directly compared to the above as it is not the maximum average, but it is a statistical cut-off number that ensure no load exceeds that pressure, backing out the average from that cut-off and assuming a standard deviation similar to military ammunition yields a maximum average around 55,000 to 56,000 psi, similar to SAAMI and M193.
And, nobody is using C.U.P. pressure measurement anymore, so please, nobody bring that up...