Bullet size maybe, in big game rounds, but bullet type ALWAYS. For many years some major factories made some horrific factory bullets and ammo. That is when my hunting partners and I went to reloading. Now factory ammo is just as good, if not better than reloading. A good hit with a bad bullet = nasty results. This I have seen this more than once. That's why I believe that butchering your animal, or watching it done is so important. Recovering the bullet, or it's parts (not good) if possible, studying the trauma and damage to the animal you kill tells the tale.
Any head shot on most big game is Very Unwise (I learned this the hard way, after being told so by my mentor). Sooner or later, you WILL shoot a animals jaw off, and not kill it. God willing you will be able to track the animal and kill it, as I did. If not it will die a terrible death.
We all want the animal BLAM-DEAD ON THE GROUND. (Some of today's ammo ads even state it, which is CRAP) When you hunt many seasons you know that does not happen all, or most of the time, no matter how hard one works at it.
Hunting with Wolves - by Michael Lukas, in the new Big Game Edition of Gray's, is well worth reading. His statement about "finger on the trigger", is just about as close to perfect as can be stated.