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I'm rusty on my physics but let's think about the diagram. You've got the same mass projectile, the same powder, and the same barrel length. The main change is the diameter.
Assuming decent rifling and the smaller caliber doesn't keyhole, it will have greater sectional density and theoretically better penetration. It could tumble after it enters but that could be a good thing for "stopping power". (I translate that loosely as the chance of doing damage sufficient to render an animal immobile or incapable of attacking.)
Assuming the same, the larger caliber should at least make a bigger hole.
One last question is how the volume change in the barrel will affect expanding gasses behind the projectile. I'll leave that for someone smart to answer. =P
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