This is again a somewhat easy choice to make. If you plan on running only (or mostly) military ammo through your rifle, just get a USGI 5.56 NATO chamber. Many people want to be able to run anything, which they can with a NATO chamber, but for more all around accuracy across a variety of 5.56/.223 ammo, the .223 Wylde chamber is the easy choice (or Noveske Match Mod O). Both were designed to bridge the gap between .223 Rem and 5.56 NATO and they do it well. It is almost exclusively the only chamber used by the top barrel manufacturers. Most chambers will accept most rounds of the 5.56/.223 family with no problem, but for the ultimate in accuracy and reliability you have to perfectly match the round to the chamber. Additionally, you should not run 5.56 NATO ammo in a .223 Remington chamber. Many still do, but the closer rifling and steeper leade creates pressures that exceed specs. Can you get away with it? Yes, maybe for a while even but that is not a failure I want to be around for when it happens.
There are some compelling articles, like this one that point out the fact that while SAAMI specs/dimensions are different between 5.56 and .223 chambers, there are only a few manufacturers that can ream a chamber to the kind of tolerances that would appreciate those differences. Even from the same brand, you might get 3 chambers listed as .223 Remington, but in actual fact the variance between them is bigger than the difference between .223 and 5.56.
However, to me that is further proof you should not tempt fate with 5.56 in a .223 Rem chamber. It just increases the chance of a kaboom if you are already over pressure and then they reamed the chamber in a such a way to further increase that pressure.