The two rounds have two distinct uses. The .223 is intended to defend oneself from mass attack (i.e. Katrina, L.A. Riots). Frankly, unless you are in the military it has very little use outside of that.
Funny, I always thought the .223 Remington cartridge was initially designed for long-range varmint hunting, and the 5.56x45 NATO cartridge was derived from the .223 Rem for making people dead.