One bullet isn't always going to put a guy down, particularly not a SMG or pistol bullet. But the same is true even for a 7.62 or a 5.56.
The actual force of impact of a bullet isn't going to knock down a target. The momentum imparted to a target when it is hit with a rifle bullet is similar to the amount of momentum that a well thrown baseball or cricketball would impart, it is just spread over a much smaller area
The human body can lose about 1-1.2 litres of blood before shock is induced an consciousness is lost. The only certain way to incapacitate an attacker is to cause significant damage to the central nervous system, or cause enough loss of blood to shut down the attacker's higher (and potentially lower) brain functions. There are certainly psychological factors that might stop an attacker ("I've been shot!"), but depending on these is probably not a good idea, and discounts the possibility that the attacker's state of mind is altered chemically or emotionally to a point where being shot won't seem like that interesting a distraction. That means you want to:
*Penetrate deep enough to get to major organs or blood vessels. *Disrupt the tissue of those structures.
*Encourage profuse bleeding and/or CNS damage
Part of the problem in Mogadishu was that troops with the M4 carbine (mostly Delta) were issued 'green tip' semi armour piercing ammunition. Obviously SAP ammo is not going to fragment like standard M193 5.56mm ammo. A 5.56mm NATO (either M193 or M855) impacting at anything above 800m/sec will relaibly fragment, causing very large temporary and permanent cavties as well as deep penetration and large exit wounds. The 5.56mm NATO also has a tendency to tumble 'upwards' some.
The problem was that the M193 is generally fired from a M16 (20 inch barrel) and has a higher initial velocity and will reliably fragment out to about 200m, while the M855 is used with the M4 carbine (with a 14.5 inch barrel) the and will only fragment out to about 50m. Hence less temporary cavity, less chance of fragmentation and a much harder put down.