A comparison between a stoutly constructed monometal bullet and a highly frangible one isn't a fair one. You could run 45 caliber pistol bullets out of a 460 Weatherby and all you would get it a loud noise and an ghastly flesh would. Would you try to argue that the 460 Weatherby is incapable of killing medium-sized game? Or would you say that the bullet choice was woefully inadequate? The other extreme applies perfectly as well. A 223 with a 50gr Barnes Varmint Grenade is a dreadfully bad combination for anything bigger than foxes but that does not mean that the 223 is incapable of cleanly harvesting medium-sized game. The truth lies in the middle. Under some circumstances the 223 is a fine deer round. In my opinion, that would be in the forests of the West Coast, Washington and Oregon shooting blacktails. In fact, I think it would be a dandy little deer rifle on Haida Gwaii. Would I want it on the open prairies of Saskatchewan and Alberta for big Mulie bucks in November? Wouldn't be my first choice by a wide margin.
Velocity can play a part in quick kills, but a complete understanding of the mechanics of death are required. Death is caused by exsanguination (bleeding out) or CNS disruption. Given all the givens, the more damage you can do to the major components of the vascular system, the faster an animal will bleed out. So all things being equal, a bullet that does massive damage to the heart and aorta will cause lethal blood loss faster. High velocity tends to cause more dramatic expansion as compared to a similar bullet at a lower velocity. More dramatic expansion can (assuming adequate penetration) cause more damage to the vital organs which causes faster blood loss.
As it relates to disruption of the CNS, velocity plays only a peripheral role. Increased velocity flattens the trajectory which results in easier hits to the relatively small targets that make up the CNS (brain and spine forward of the point of the shoulder). All the bullet needs to do is penetrate to the brain or spinal column and the result is nearly instantaneous death. But it doesn't need to be going fast to achieve this. You could kill a deer just as quickly by driving a knitting needle into it's brain using your bare hands (though that would raise some disturbing questions about a person's state of mind). Velocity only aids in disruption of the CNS when you are using a frangible bullet and miss the target but a lucky piece of shrapnel severs the spinal column. This is not skill or a benefit of any aspect of the system, it's just dumb luck that cannot be relied upon or given any weight in the argument.
So to compare apples to apples, if your GF had been using a 139gr GMX I don't believe that you would have been able to tell a bit of difference between her deer and that of your daughter, given ideal shot placement which severs the spinal column. Nor does a high impact velocity guarantee better results. In the end, it's all about using a properly constructed bullet and putting the said bullet in the proper place with enough retained energy to ensure adequate penetration of the vitals.
Sounds so easy when you boil off all the extraneous broth!