I agree with gangog56
There are only two reasons you should be concerned about the difference: Brass wall thickness, and OAL of the case.
The reason brass wall thickness is a concern is because the thicker wall reduces overall volume, thus increasing pressure under ignition.
The OAL is a concern only because the throat of the barrel on a .223 and a 5.56 have a different leade space. As long as they are all trimmed to spec for the lesser dimension, there is no problem.
I have found that the Military 5.56 brass is usually cryptic, and DOES NOT have .223 stamped on the head. IF the brass is stamped .223, I load it for the higher pressure loadings for bolt action rifles. If it is stamped any other markings than .223, I reserve them for AR 15 pressure loadings.
Of course, this demands good record keeping, and the separation of the different ammos.
The simplest way to go about it is to simply load ALL of your brass to mil-spec. loads, assuming the thick wall cases, and then you have no problem. The drawback to this is the inability to maximize the loads for your accurate bolt action rifles. As always, it's a trade-off.