With any non-match grade AR, you're most unlikely to see any difference between .223 or 5.56mm in the 5.56mm chamber within 100 meters. This would be true even if the shooter was Olympic grade.
Given benchrest rifles (20 lb monsters with 2 oz triggers fired from machine rests) in the hands of experts in that sort of thing, you might see a difference. That difference wouldn't matter to the vast majority of shooters.
The difference in bore contact between 55 and 62 gr FMJBT bullets isn't significant.
The difference in terminal effect between the two is. As JaPes notes, the M193 tends to swap ends, break at the cannelure and fragment upon tissue impact. The steel insert of the M855 is due to a requirement to penetrate a specified protective helmet at X00 meters. As a result, M855 is much less disruptive of tissue.