What can be said about the buoyancy force if the volume of the bodies is the same?

If the volume of the bodies is the same, then the buoyant (Archimedean) force will also be the same, since it is proportional to the volume of the immersed body. The only difference is that the body whose weight is less than the buoyancy force will float to the surface, and the body whose weight is greater than the buoyancy force will sink. If the pushing force is equal to the weight of the body, then it can be at any depth in the liquid in which it is immersed.