No dimension difference, only difference in the case is the 5.56 has beefier webbing at the case head to handle higher pressure. The .223 chamber's dimension's are tighter, which is supposed to give better accuracy. The 5.56 chamber is a little bigger and throated differently to handle higher pressure.
If you do a google search you can find all of this information.
If you do a google search you can find all of this information.