Ever since the Vietnam war, there has been an ongoing debate over the stopping power of the 5.56mm round used in the M-16 assault rifle. Some of the same complaints, and arguments, have been revived recently as a result of the heavy combat that's taken place in Iraq and Afghanistan. This was the first time, since Vietnam, that the 5.56mm round has seen a lot of action.
During the Vietnam war, there were reports of enemy troops not going down when hit with a 5.56mm bullet, while troops using rifles with the larger 7.62mm round reported far fewer such problems. Keep in mind that many of the NCOs in Vietnam had fought in Korea and World War II, using the M-1 rifle (and it's 7.62mm, or .30 caliber, round) and had lots of opportunity to compare the "stopping power" of the two different bullets. But there was also a lot of support for the lighter M-16, with its lighter (especially to carry) ammo and flatter trajectory (because of its higher speed). The Vietnam war ended without any pressure building to go back to a larger cartridge. While some veterans believed a larger bullet was needed, most were content with the M-16.
On paper, one measure of "stopping power" is the joules (or foot pounds, where 1000 joules equals 737.6 foot pounds) a bullet transfers to whatever it hits. Joules is a measure of energy (the weight of the bullet times the velocity as it comes out of the barrel.) On the low end, we have the .22 caliber long rifle, with 190 joules of hitting power. This is enough to snag squirrels and rabbits. A .22 can kill people, but only if they are hit in the right place. For serious killing, the most widely used rounds up through World War II were the 7.92mm (4670 joules), the .303 caliber (or 7.7mm with 3320 joules), the .30-06 (7.62mm with 3660 joules), 6.5mm (various models, 2300-2700 joules) and .30 caliber US Carbine (1070 joules). That period also saw widespread use of submachineguns (automatic weapons using pistol rounds.) The most widely used of these were the 9mm Parabellum (583 joules), 7.62mm Tokarev (499 joules) and .45 ACP (11.4mm with 450 joules). After World War II came two new cartridges that have dominated military rifle use, the Russian 7.62mm M1943 (1890 joules) and the 5.56mm (1780 joules).
But there's a major problem in just using joules, and that is how much of that energy is actually applied to the person being hit. A smaller, faster bullet has a tendency to just go through someone. This does damage, often fatal damage, but if often does not slow down a highly energized soldier. A larger bullet, especially a blunt one, will be more effective at "stopping" someone. Thus the popularity of the U.S. .45 caliber pistol round. Although it has less energy than the 9mm round (450 joules compared to 583), those who have used both insist that the .45 is far more effective than the smaller and faster 9mm. Part of this has to do with the fact that the .45 (11.4mm) bullet hits with a 60 percent larger (as seen head on) area, thus it applied more of that energy to the target. This explains the greater likelihood of the .45 caliber bullet "knocking down" whoever it hits. The same physics applies to rifle bullets (although they tend to have pointy tips, unlike the blunter ones for pistol pullets.) A 7.62mm bullet is 88 percent larger (head on) than a 5.56mm one.
But the 5.56mm bullet has one considerable advantage; cavitation. At higher speeds, like those the 5.56mm round employs, causes more flesh to be displaced as the bullet enters a body. Compared to a heavier, slower moving traditional (7.62mm or .30 caliber) round, the 5.56mm round not only displaces more flesh, but begins to tumble, which further increases the internal damage. Without seeing the bullet, a military surgeon can immediately tell which type of bullet did the damage. These doctors will tell you that a 5.56mm round, on average, does a lot more damage. Especially at closer ranges (under 500 meters.) And it was worse with the earlier models of the M-16. These had rifling that imparted a slower spin to the bullet, this meant that the round was even more unstable when it entered the human body. But the slower spin made the bullet less accurate at longer ranges, so the rifling was changed, gradually, from 1:12 (the bullet rotated once every 12 inches) to 1:7. It was found that the damage to enemy troops was still sufficient, and accuracy at ranges over a few hundred meters was much better. Note, however, that at longer ranges, the 5.56mm round slowed down to speeds closer to those of the heavier 7.62mm round, and this greatly reduced the cavitation and tumbling effect. Thus at longer ranges, you had more instances of enemy soldiers taking several hits without going down. But at more typical combat ranges (under a hundred meters), the damage from one 5.56mm bullet is substantial. However, it's also possible for a 5.56mm bullet to hit somewhere (side of the arm or leg, or chest) and go though insufficient flesh to do much cavitation, much less tumble. The shooter would note the target jerking a bit, but continuing to advance. Thus would be born another first hand witness to the "ineffective 5.56mm."
At the moment, the round with the most stopping power (on paper and witnessed in action) is the .50 caliber (12.7mm) round used in heavy sniper rifles and heavy machine-guns. This bullet generates 16,914 joules. Guaranteed to stop anyone, or just about anything, it hits. In combat, overkill is good.
Much experimentation has taken place to develop the "perfect bullet" and at present it appears to be something between 6mm and 7mm. But the only time you get to see what really works is when there is a war. But even then a lot depends on where you are fighting, and who you are fighting with. If combat is in the wide open spaces, the fast, light 5.56mm rounds are at a disadvantage. But in jungles and cities, the 5.56mm is very effective. If you are fighting fanatical type opponents (like the Japanese in World War II, or Islamic radicals today), you want as many joules as possible, on bullet designed to stay in the target.
The joules do count. In the Pacific during World War II, the lightweight U.S. .30 caliber carbine (using what was basically a pistol cartridge) got its bad reputation. The bullet fired from the carbine only had 1070 joules, less than a third of the joules generated by the more powerful .30-06 of the M1 Garand rifle. In Europe, where most combatants were only too happy to get wounded and evacuated to the rear, a hit from carbine bullet would drop most people. But if you are really determined, getting hit by a carbine bullet is often just an annoyance. But the 5.56mm round changed that. While small, it was fast, and designed to tear you up inside. That's more than just annoying.
So which kind of round is best? Well, it really depends. But there are more combat veterans swearing by the 5.56mm, than swearing at it.