The 223 can be fired in both the 5.56 and the 223 chamber. So, 223 dies would be the safe way to go--if it really would matter. Just use 223 data from your load book.
There have been a number of articles written regarding the differences, but the bottom line is: 223 is safe in a 5.56, and 5.56 may not be safe in a .223--unless the 223 has a chamber, such as the Rock River Arms' Wylde chamber or the Ruger Mini14, which are designed to handle both.