Others here are clearly more knowledgable than I, and much better shooters as well. But I was experimenting with a half dozen different factory rounds at 50 and 100 yards this past weekend with my 20" Bushy, so I'll chime in anyway.
I shot Win white box 55-grain .223s, Win white box .223 varmint loads (can't remember, I think they were 47-grain??), Federal American Eagle .223s, Federal packaged Lake City 5.56 XM193s, Win packaged 5.56 Q3131As, and something else, too, but I can't remember what it was.
Now, in fairness to me, this was with factory iron sights, mediocre 47-year old eyes, a flimsy plastic lawn chair as a rest, shooting one shot every second, and it was the first time I had shot the gun outdoors.
At 100 yards, my results were not helpful; just embarassing. (I did later get a 5-shot quarter-or-nickle-sized group with my scoped A-Bolt, so I'm not completely incompetent.)
At 50 yards, however, my patterns turned into groups. All of the .223s shot into 6"-diameter circles at 50-yards. The two 5.56 loads, however, shot into 4"-diameter circles. I did one 20-round slow fire test with the Lake City rounds (about one shot every 10 seconds), and got a 3"-diameter circle. Hey, I know that sucks, but that's what happened, and I wasn't unhappy with it given all the circumstances.
So, my conclusion is that if the gun is designed for 5.56 rounds, it will probably shoot factory 5.56s better than .223s. That's not exactly a news flash.
The place we bird hunt, in the western part of the state, is really the only place I can test this stuff out (um, no, not on the birds), and last weekend was my first chance. Over the next 5 or 6 weeks, I will definitely be refining these "tests" and getting more familiar with the gun. I'm really looking forward to it, but, man, one really does go through the ammo out there...