The only difference is basically chamber pressure. I'd pick up some surplus of 5.56 and a box of .223 and see which you like more.
5.56 is known to have a higher velocity than the .223... either way it should shoot about the same up to a certain point.
I just want to clarify, this poster is NOT suggesting that you shoot 5.56 in a .223 chambered weapon.
He is referring to if you have a 5.56 weapon.
Find out what your weapon is, and then shoot that.
What brand is the upper? Some manufacturers will specify .223, others are good with either.
Check in the owners manual, or if you dont have one, maybe somebody on this board will have one for that make.