Between my sons, wife and I, we have killed a substantial number of Mule Deer and Elk over the years with the calibers you mention.
The only animal I have not revcovered that I shot with a rifle was a bull Elk I shot 3 times inside of 50 yards with a 30-06. All three shots were in the boiler room.
I re-barreled the 30-06 to 25-06 after that and started hunting EVERYTHING I hunt with the 100 grain Sierra bullet. I've never had to track an animal since then.
In our experience, we have shot our animal in broad-side situations, shooting them in the lungs. The fast bullets cause so much hydrostatic shock that it vaporizes the lungs.
Keep in mind that we are very good shots and we don't take "iffy" shots.
By the same token a 300 MAG is useless if you don't place the bullet in the right place...close only counts in horse-shoes and handgrenades.
The light recoil of the 243/25-06 class weapon also aids in avoiding flinching from recoil. Again, you can't hit anything if you are trying to out-run the recoil.
I think that the bigest issue is really the individual persons ability and proficiency with their weapon. By the same token, I wouldn't use either caliber for LARGE bear species, or dangerous game. If I was hunting Griz or Kodiak, I'd be packing a 375 class gun.