Guys, you're really arguing this from the wrong angle. You're talking energy and tissue damage when really if you want to get your head into this you need to talk biology.
there is only one way to kill an animal - shut down it's brain. Everything else is a means to that end. Stopping it's heart works because it's brain shuts down. A cns hit works because the brain can't talk to the body any more. Blowing out its lungs stops oxygen flow to the brain. You can disable or immobilize the animal other ways, but really it's about stopping the brain.
And btw - cardio-pulminary systems are very different from animal to animal. A grizzlie's system is far more 'rugged' than a deers for example - grizzlies can go longer without their blood actually pumping without dying. Which is why cartridges that leave deep heavily bleeding wounds tend to be favoured, (they create a very sudden drop in pressure) and why you have to look at immobilizing the animal long enough for it's brain to shut down. What drops deer the best may not be what drops grizzes the fastest - so you have to remember to compare apples to apples.
A slow, fat bullet knocks a plug out of an animal and causes less damage to the tissue around the wound channel - which means less bruising and far more blood loss. Great for creating a very sudden drop in blood pressure which is a fantastic way to get an animal down fast.
Fast bullets that mushroom and make a nice shockwave tend to destroy a lot of tissue thru cavication and the transmission of the shockwave inside the animal (the barrel shaped bodies of deer and moose for example are excellent in containing the shockwaves and giving you CNS damage that will immobilize the animal while it dies), and they tend to be more likely to create clots and damage that lead to immediate brain disfunction. Deer have nice big lung areas and need lots of oxygen to function properly and cannot survive much damage to their cardio systems, and thats why smaller faster rounds that damage lots of tissue and cause heavy bruising and cns damage are noted for giving 'bang-flops'.
Slow bullets tend to penetrate softer tissue better. Fast bullets (if they hold together) tend to penetrate and shatter bone better, but due to the increased resistance on impact can perform less well on heavy soft tissues if they deploy too quickly unless they have lots of energy to spare.
This is a little simplistic of course - but you get the idea. There is no 'best' method - you need to look at how the bullet is trying to affect the biology and disrupt the animals functions, and determine if the cartridge in question is doing it's job well. There are slow fat bullet cartridges that are better than others, there are fast thin bullets that are better than others, and there is of course a point of diminishing return. And it will be slightly different for each species of animal.
Look at any round you like, look at how it's trying to disrupt the animals systems and how it will affect its' brain (blood loss, cns, clotting and bruising, dissue disruption, etc) and then look at the animal and how it's designed (how much tissue will you need to get thru, what kind of bone and fat will you have to get thru to , and you'll tend to get excellent results every time.
And the fact is - very few animals will long survive a good hit from ANY modern centerfire cartridge that's loaded with an appropriate bullet that maximizes it's characteristics if you hit it in the vitals. So with the possible exception of dangerous animals, we're arguing over something that makes very little difference. It's interesting to talk about - but really it makes virtually no difference in the field.