5.56, I believe, has a little higher pressure cap meaning you can get a little more velocity. But I’ve heard that .223 ammo and the chambers for them are made to tighter tolerances which usually results in slightly better accuracy. In both cases it doesn’t seem to be enough difference to be noticeable unless you’re shooting competitions or pushing your rifle to its max.
I stick 5.56 rounds in my bolt .223 gun with no signs of high pressure.
All the reading and told knowledge
The chamber is a hair longer and more spacious in the military 5.56 chamber to allow for the longer tracer rounds and rounds that have dirt or dust on them to feed and extract as necessary in combat situations. In a bolt gun I wouldn’t sweat it. If it’s an semi auto platform I would by a 5.56 chamber and let it all fly.
Brass can be thicker in a 5.56 casing = less powder capacity. The worry is someone loads a thin walled .223 casing recipe in a thick walled .556 casing and you het high pressure.