Interesting stuff here guys. I've shot deer, antelope, and elk with everything from a .22 Hornet (only deer) to a .338-378. And each one has reacted differently. Some run, others collapse, some flip over and flop... one thing that I can say for sure about most of the hunting shows where you are seeing instant DRT's (dead right there's) is that most of those guys shoot to break an animal down via crushing major skeletal forms (shoulders) and nervous system centers (spinal cord). For two reasons; one, it ensures recovery of the animal and two, it makes for great T.V. when an animal is killed instantly. Many people do not understand that when a heart/lung shot animal runs off that it is dead on its feet. They assume it is suffering and not in a state of deep shock. Therefore, killing an animal instantly is appealing to both the hunting and non-hunting public.
However, the question remains, how is this done? This can be easily accomplished via a high shoulder shot that strikes the animal on the point of the shoulder two-thirds up the body. A hit from any high velocity, well constructed, caliber appropriate, bullet in this region on ANY mammal will drop them instantly with thier feet tucked and rear hitting the ground followed by their head hitting, Hard! This method works on any and all animals for the simple reason that the bullet is destroying three vital systems; skeletal, nervous, and circulatory all at the same time. The shot placement formula listed above comes from a combination of years of practicing it after reading and watching how to do it from African and North American Writers that span Capstick and Keith to O'Connor and Boddington.
When shot through the ribs behind the shoulder and under the spinal cord an ungulate or predator is being struck in only one vital system, circulatory. Therefore, it does not matter how large the caliber is, there is a high probablity that the animal will "run off" and die. I say that caliber does not matter, assuming one is using a game appropriate caliber (deer/antelope .25-06 - 300, elk/moose 270-375) because a bullet at high velocity that does not break bone and relies and soft tissue devastation via hydro-static shock alone rips through an animal at hundreds if not thousands of feet per second and therefore as is quite often the case as I have experienced on deer sized game, the larger the round the less tissue damage there is and the greater the chance the animal will "run off." I have seen this numerous times when killing deer and antelope with my various .300's, .338's, and big bore lever guns, not that these are not great all around game cartridges because they are, however, they do seem to perform better on game that provides a more substantial body mass (elk/moose/bears) for the bullet to dump it kinetic energy into via expansion and velocity loss. With that said, I've experienced more DRT kills on deer sized game with my .257's, 270's, and non-magnum 30's than with any of my super fast, "HUGE" rounds like my .338-378 or .300 RUM. Unless! I break them down as written about above OR, and here it comes... I am using a fragile and therefore bullet designed for maximum soft tissue destruction. For example, the Nosler Ballistic Tip, Hornady SST, or any of the billed "Varmint Bullets." All of these expand very rapidly and dump massive amounts of energy into a small space and therefore "shock" an animal's nervous system without breaking it down. The arguments for and against these bullets is long and storied but the point is that when kept away from heavy muscle or bone they kill very quickly and cleanly. They are simply not designed to break an animal down by breaking bone though they will do it at proper velocities.
I think we could all take a lesson from the T.V. guys on this one. While there is nothing wrong with shooting for the lungs due to its being a large target and 99.99999999% effective at killing game and therefore, widely and rightly practiced there is a strong argument for breaking animals down by crushing and destroying all three vital systems with one bullet. This is expecially true with dangerous game or in situations where game cannot be allowed to run, e.g. fences, cliffs, water, etc. All hunting situations are different and each calls for specific determinations of shot angles and placement but I for one will continue to shoot "high shoulder" and watch 'em drop hard!
Shoot straight brothers and sisters.