.223 Rem vs 5.56 NATO is probably one of the most discussed and contentious reloading topics ever.
The differences between the two cartridges are minuscule, but important, and the actual answer as to whether or not it is safe to use 5.56 NATO in your .223 rig is; It depends 
Ultimate Reloader gives one of the best rundowns that separates fact from myth.
Here is another good, but less technical explanation.
