There is a pressure spec. difference between 5.56 Nato and .223 Remington. I don't know how great the difference is but I spend a fair amount of time at AR-15.com and have learned that a difference exists. As I shoot an AR I never bothered to investigate any further.
What config is your remington? If you've got a bull barrel & a scope, I'd either hand load or try a bunch of different premium ammo to see which was the most accurate from my gun. The xm193 is great "volume of fire" ammo for an AR, but I don't think it's really match grade one-hole ammo.
I'd go through some loads from remington, federal, speer, hornady & the like & see what I can get the tightest groups with. That's really the fun of a gun like that.