The throat is longer in the 5.56, other than that the chambers are identical or should be.

As far as the ammunition the 5.56 NATO has a higher working pressure than .223.

Here is all you ever wanted to know about the differences between 5.56 and 223 as well as variations of the 5.56.
http://razoreye.net/mirror/ammo-orac...cle_Mirror.htm

308 Winchester and 7.62x51 NATO are just the opposite. The NATO round has a lower operating pressure than the 308 Winchester. There are a lot of military rifles chambered in 7.62x51 that are warned against shooting commercial ammo in for safety reasons, HK and their clones come to mind but there are others as well.

Dolomite