Certainly Doc is right about the superior terminal performance and intermediate barrier capability of the 6.8.
On the other hand, the .223/5.56mm's advantages include better ammo availability, lower ammo cost(lowest cost factory 6.8mm ammo is about two to three times the price of lowest cost .223/5.56mm factory ammo), greater availability of firearms chambered for it, greater availability of 5.56mm caliber-specific AR parts(bolts and barrels), greater options in quality AR mags in .223/5.56mm(PMAGS, Lancer, GI 30 rd, NHMTG 20 rd GI, etc) than 6.8(Barrett and PRI), lower cost of 5.56mm quality mags, and lower recoil. I'd expect greater durability with a 5.56mm rifle than a 6.8mm, all other things being equal, but I have no hard data on that.