Very good discussion topic, 500grains!

IMO it depends a lot on whether the original cartridge was capable of killing by 'shock' in its 'standard' form.

I tend to apportion cartridges into two different performance categories: those that have a significant 'shock' component to their performance, and those that don't. In my experience the distinction would occur at around 2300 to 2400 fps muzzle velocity.

A significant part of the success of the .375 H&H at 2500 fps or more is probably attributable to shock. Loading a heavy bullet at only 2200 fps will take away the shock component, and move it into the second category.

If a cartridge turns up less than 2300 fps, it kills by wrecking vital organs and/or haemorrhage, so changing to a heavier bullet at lower velocity will not reduce performance. In fact, on big game where vital organ damage depends on good penetration, a heavier bullet will be a distinct improvement.

When hunting truly big game, the 'shock' component of an 'over 2400fps' bullet is probably worth almost nothing, so for pachyderms I'd say heavier bullet at lower velocity every time.

For plains game though, take away that 'shock' component, and expect them to run up to a hundred yards or more before dropping (if you miss the spine or shoulder-joints). In some cases this might result in a lost animal.

I should add that I prefer the heavy slow bullets for the vast majority of my hunting, because of the ever-present chance at a buffalo. ...but I am continually surprised at just how far a big boar can run after being spudded through the heart or both lungs with a 400 to 650 grain low-velocity bullet, when the same shot with a .243 would have been 'lights out' on the spot!