I'm not expert. Let's get this out of the way first.
However I've read, been told, and had confirmed from a Rock River Arms distributor that the .223 version is a civilian version round and the 5.56 version is the military version and the only difference is the 5.56 version (nato) runs at higher case pressures which is of no consequence if you have a barrel rated for NATO/5.56 round.
But if you have a .223 rated barrel and run 5.56 rounds through it,... well I can't say for sure your rifle will explode but overpressures aren't exactly optimum conditions and would tend to void any warranty.
You other fellas can correct me if I've been misinformed.