Anyone using the term "knock down power" is ignorant of ballistics. Mr. Newton proves it. Physics rules. Any bullet that can "knock a man down" at impact would also knock the shooter down. Google the guy wearing a vest who gets shot with the 308 point blank while standing on one foot and doesn't even wobble to illustrate the principle.
However, increased terminal affect can be realized with a larger caliber. But once adequate penetration is realized, bullet design is much more important than caliber. For example, a 6.8 FMJ will be less effective than a 5.56 with a Barnes TSX. But even with that said, shot placement is paramount. The only way to physiologically knock some one down with a shot, is a hit to the central nervous system (brain/spine,etc); and caliber won't make a difference here. Now if someone drops after being shot anywhere else, that can be attributed to psychological factors. Even with a hit that explodes the heart, there is still enough residual blood in the brain to function for 7-10 seconds. If you have ever hunted deer, you have probably witnessed this phenomenon.
So to answer your question does the 6.8 have twice the knock down power of a 556? No. Is it more terminally effective than 556? With equal bullet types, likely due to a slightly larger wound channel that it can create because of the larger caliber. But all this talk is in reference to human targets. If we start talking big game hunting, then we will have to discuss other factors, primarily penetration due to more momentum of the heavier projectile in the 6.8 giving it an advantage over 5.56.