Quote:
Hello. If two barrels of the same length where loaded with the same amount of powder and with projectiles of the same weight, but of different calibers, will then the stopping power of the guns be equivalent?

Factors....
same powder charge
Same length barrel
Different bore diameters
Same bullet weight
The larger bore will have a larger velocity.....but the smaller bore could have a higher bc. It depends on too many other factors to be sure. It will likely be about the same, so the larger one has a significant advantage due to same bc and higher velocity.
Stopping Power  For this, stopping power has to be defined. I would define it as the energy expended in the animal through expansion and tissue damage.
The larger caliber will have more velocity meaning higher kinetic energy at impact. Assuming same bullet construction, the larger diameter will expand easier due to frontal area. This too is a win for the larger caliber.
Answer: Caliber wins! This comes at a price......more recoil!