Since the 1960s, when the U.S. began  using two calibers for its rifles and machine-guns (5.56mm and 7.62mm), there has been a debate over the effectiveness of the lighter 5.56mm bullet. Initially, U.S. Army officials took it on faith that the 5.56mm round could do the job. Hunters, however, rarely used the 5.56mm (.22 caliber) round on game that weighed as much as a man. Nearly all hunters used bullets of at least 6.8mm (.270 caliber), and most preferred 7.62mm (.30 caliber) or a shotgun firing an 18.5mm (12 gauge) solid slug (a deer slug.) The advantage of the 5.56mm weapon (the M-16) was weight. Not so much the weight of the weapon (only a pound or two lighter than 7.62mm rifles), but in the weight of ammo. Troops going out carrying 200 rounds of 7.62mm ammo would be carrying 12.2 pounds of bullets. But with an M-16, they could carry 700 rounds for the same weight. Actually, they would carry less, because of the weight of the magazines, but that still gave an infantryman more than twice as much ammo for the same weight carried. 

In the last four decades, there have been constant complaints from the troops about enemy soldiers hit by 5.56mm bullets, who kept on coming. These accounts were not urban legends, but they were not unique either. As far back as 1900, during the fighting against Moslem rebels in the Philippines, there had been complaints of enemy fighters getting shot and continuing to attack. From this experience, the then standard army pistol, a .38 caliber (9.65mm) weapon, was replaced by a .45 caliber (11.4mm) one. In the 1990s, the .45 was in turn replaced by a 9mm pistol. There were a lot of complaints about that, but 90 years experience demonstrated that you should not depend on a pistol in the heat of combat. If you want protection against fanatics, take a shotgun with you. 

Examining the experience of hunters, and soldiers in many other wars over the past century, one can conclude that caliber is not as important as where the bullet hits, and what state of mind the target is in. The Russians, and professional assassins, frequently use .22 caliber pistols or rifles to take out victims at close range. Two in the head, you know hes dead, is their mantra. At the other extreme, there have been cases of troops losing a limb to a .50 caliber or 20mm shell, and continuing to fight, for a while at least. This points out that, if you shoot someone in the brain, or spinal column, they will go down, no matter what caliber the bullet is. But if the target is energized, with the adrenalin pumping, you can shoot them several times, in non-vital places, and they wont immediately notice the injury. Such incidents were widely reported during both World Wars, when most bullets fired were equivalent to the current 7.62mm. 

Some hunters go after deer, especially white tail deer, with 5.56mm weapons. But most prefer a larger 7.62mm weapon, or a shotgun firing solid shot. If you are a very good shot, you can regularly bring down deer (who weigh about as much as a human, between 100-300 pounds, but with a lot more muscle and speed) with a 5.56mm round. But the key is getting the heart or lung shot. An additional advantage of the 5.56mm rifle, is that the lower recoil enables you to get two or more shots at the same aiming point, because the first one wont knock you off your aim. However, the majority of hunters are not sharpshooters, and prefer the harder hitting 7.62mm rifles, or 12 gauge shotgun.

American infantry are much better trained than they were in the 1960s. Many of the troops back then were draftees, in for only two years. Today, most grunts are in for three or four years. A year or two of additional training makes a big difference, especially with the better scopes and marksmanship training methods used today. For that reason, theres a movement within the army to switch from 5.56mm to 6.8mm. This would mean that ammunition would be heavier (almost twice as heavy as current 5.56 rounds), but the feeling is that the heavier bullet would be more accurate at longer ranges, and more likely to take down whoever it hits. The problem is, there has never been a scientific study of this issue. You cant get people willing to be shot, in different places, while at different levels of agitation, to see how long they can continue to move or fire their weapons. The anecdotal evidence is, well, anecdotal. It is a fact that shots in the brain and spinal column will definitely take down your target. The 6.8mm round will probably be more likely, than the 5.56mm, to stop most enemy troops. But will it be worth the risk of carrying less ammo? Often troops use ammo just to make the enemy keep their heads down, or prevent them from moving. In these situations, volume is more important that accuracy. No studies have been done of this aspect of combat, although there is much anecdotal evidence showing how important this kind of fire is. 

But one thing is certain, when it comes to bullets, its not caliber or hitting power that counts as much as where it hits.