HowStuffWorks explains that a .45 caliber bullet is slightly larger than a .357 caliber bullet. Caliber refers to the diameter of a bullet or barrel in inches, which means that the .45 bullet is approximately .093 inches larger than the .357 round.
While bullet caliber indicates the size of a given slug, it is not the most important factor in determining the stopping power of a bullet. While the individual characteristics of a bullet vary among manufacturers, .45 bullets are heavier than .357 rounds, and they travel somewhat slower due to their larger mass. The .357 magnum rounds also use a higher-powered gunpowder load, increasing the bullet's muzzle velocity and momentum.
Ultimately, the effectiveness of a bullet depends on its ability to transfer its kinetic energy to the target. The design of a bullet can make it much more efficient at transferring this energy and causing the tissue and organ damage necessary to put down a target. Full metal jacket and other solid rounds are designed to maintain their shape and structure as much as possible when they hit a target, causing relatively smaller wounds and only transferring much of their kinetic energy if they hit dense bone. Conversely, hollow-point rounds deform and spread once they hit a target, causing massive damage and trauma in the target.