Even with the increased leade, the effective case capacity difference between the 223 and 5.56 is small and very little, if any, velocity difference will be seen between the two when used in their respective chambers.
If I look at Barnes' website and reference their reloading info, listing the same powder and bullet, the 5.56 has maybe 3-4 grains more powder and hits a velocity almost 200 FPS faster.

I agree that the pressure of the shot, .223 round in a .223 chamber vs a 5.56 round in a 5.56 chamber is the same, the 5.56 has a higher velocity. It's common knowledge that a 5.56 round in a .223 chamber can lead to dangerous pressure levels.

I just haven't seen any data to suggest a .223 round from a .223 chamber hits the same velocity as a 5.56 from a 5.56 chamber.