I've never taken a 500yd shot on game, and hopefully never will. I have put a lot of different bullets into critters between 10ft and 300yds.
In my experience pretty much any cartridge .243 to 30-06 will do the job equally well when decent shot placement is used. Where you gain some advantage with larger, heavier bullets is when you screw up.
I like rounds that launch relatively heavy for Cal bullets at 2800-3100fps, and this includes most small bore Magnums. If meat damage is a concern, shoot a harder bullet, or don't shoot them in the eaty bits.
Bang flops won't happen every time, no matter what you shoot, but cause more damage and your more likely to have a dead critter quicker. This becomes more important the farther away your target is.
I chased a 40lb goat over a mile, because we couldn't connect a second shot on it after my buddy hit it with a relatively slow .243 (100 at 2800) at 300ish yds and it tumbled and ran. The shot wasnt that bad, but the exit wound was only about an inch, and only one lung was damaged.
Faster, softer, heavier bullet and the exit would have been double or triple that, and internal damage much more.
Would it have been any deader? Nope, but I bet it woulda been dead, quicker.