Not a single caliber - pistol, rifle, or shotgun (gauge) - is a guaranteed manstopper. For any caliber you care to mention, someone can tell a horror story about how some scumwad took five hits from a .50 Browning and kept coming.
However, the .223 is far superior to the .45 in whatever sort of stopping power you wish to measure. At the relatively low velocities of pistol calibers, the only wound channel that really counts is the permanent hole that the bullet drills through the body. At rifle velocities (3000 fps or so) that little .223 bullet stirs up quite a fuss, and blows comparatively HUGE holes through tissues, organs, etc, particularly if/when the bullet yaws inside the body or if you're using soft point ammo.
There is zero question that the .223 is the better caliber to take to a gunfight, given the choice.