Does 357 bullet do more damage than 40 caliber?

Depends on the bullet type

Even more important is shot placement, and penetration. No matter the bullet or caliber, the important thing is to damage a vital area. An example of vital area can be the heart, lung, liver, aorta, large artery or vein, spinal cord, brain, etc. Rapid blood loss, and drop in blood pressure is deadly. So to is a shutdown of the central nervous system (spinal cord and brain). Accurate shot placement, (and penetration), to the center mass is most important.