FWIW my experience has been that dropping an animal on the spot comes down to a combination of bullet placement and bullet performance. Bigger bullets don't seem to help if either placement or performance isn't up to the mark.I have, for example, had cases where a big bullet through what should have been a vital area hasn't resulted in dropping the animal on the spot, because, as far as I can work out, the bullet hasn't caused enough damage on the way through. Cases which spring to mind include a fox shot square through the chest with a .30/06, who ran away probably 50 yards into cover, and took some finding (dead when I got to him though), and some pigs shot with bullets which performed well on buffalo, but didn't seem to be opening on the much smaller pigs, resulting in quite poor killing power. Of course there also has to be enough performance (enough momentum and bullet integrity) to get in far enough to damage something important too, and I wouldn't be alone in experiencing failures on that front too.
FWIW for putting an animal on the ground DRT I prefer, as a general thing and if the opportunity is there, to put a shot into the CNS, such as either with a neck shot or shot through the shoulder blade to the spine. I've put a good number of animals of various sizes nose-first into the dirt with one or the other, including from full gallop. The bullet through the shoulder blade to the spine will often scatter bone fragments into the artery and nerve junction (brachial plexus) in that region as well. Of course the price to be paid is that you damage more meat, where that is a factor, than you would with a shot into the chest cavity. The shot to the chest also gives you rather more room for error.
I've also shot the odd critter square in the brain as it came towards me, and that seems to take the fight right out of them.
