In my opinion only difference is that with Final Round you can set it at the last bullet to make it 100% one shot body kill, so basically this Luck in the chamber is water down version only because you can't manually predict which shot is gonna do the one shot one kill to the body damage. Iron Banner and ToO Final Rounder lunatics took way too much advantage of the perk and killed it. Imagine final round and luck in the chamber rolls on the same sniper, it would break the game lol.