Excellent question.
Just check the Ramshot loading data for 223 vs. 5.56.
Ramshot TAC, Hdy BT-FMJ 55 grain bullet, max load is 25.8 grains for 3293 FPS in the 223. In the 5.56 it is 27.3 grains for 3450.
As an alternative, you could chronograph American Eagle 223 ammo vs. American Eagle 5.56 ammo. They are both made at Lake City, on the same equipment, and they do mark the boxes differently. I haven't performed that test, but it would be interesting to know
