A .45 bullet has an cross section area of 0.159 inch sq. A .357 bullet has a cross section area of 0.10 inch sq.
Since the vital object could be anywhere along the circumference, a .45 bullet should increase the odds of a nick by about 60%, assuming zero expansion. With full metal jackets and military ball ammo, and assuming equal penetration, that might account for the much better reputation of the .45 over the 9 mm/38 sp. And the old .38 specials/9mm were not +P, and wouldn't have penetrated as far anyways.
With other types of bullets, the expansion might overcome some of that advantage. Also, I suspect it isn't quite a matter of math - it might require a fairly good hit to break an artery or the CNS. In that case, the advantage of a 45 goes down a bit, but I don't know how much.
Once a bullet goes thru a body, I wouldn't expect the wound channel to allow an observer to know the caliber. The tissue doesn't evaporate, but fills in the channel and a .1 inch difference would probably be hard to distinguish.
Again, the best bet for doubling your chances of hitting something vital is to shoot twice. That suggests additional capacity is a bigger factor than bigger/faster bullets, unless you move up to a rifle. A 44 Mag may have more stopping power than a 38+P, but I wouldn't count on it. And for many of us, more practice is better than 'more gun'.