For calibers from .243 to .338 there is a greater difference in results after impact due to bullet construction, velocity and mass than is due to initial diameter. .50 BMG is in a different class entirely, as is an 88mm round from a tank.
That said, there IS a difference if comparing bullets with similar velocities and construction. Is there anyone here that would rather be hit by a 250g .338 FMJ @ 3000fps than a 55g .223 FMJ at the same velocity? Count me out on that one.
My 7m RM has reliably taken elk since 1982. My 338 WM takes them just as reliably and makes much larger holes in and out. If my .338 had the same recoil as my 7mm RM, I'd retire the 7mm RM.
No cartridge is going to put down an animal if the placement is poor enough. A few years ago I shot an elk broadside at 400 yards, plus or minus a couple, across a valley. Wind pushed the bullet back further than intended and, judging by the massive blood trail, I hit the liver. We trailed that elk over a ridge, across a valley and over another ridge. The blood trail went from ribbons of dark blood 2-3" wide and 2-3 feet long with blood chest high on the brush on both sides of the trail. The blood trail diminished to to occasional drops before finally petering out entirely as the elk approached a fence that marked the end of huntable land. With no trail to follow and no idea if the elk jumped the fence or not, we had to give up in the dark and resume the hunt the next morning. We never found the elk. I am convinced that a different bullet (like a Berger) would have done more damage to the liver and caused the elk to bleed out faster, leading to a recovery. I suspect the same hit with my .338 would have resulted in a different ending a well.
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The point is that we live in a world where incremental differences often or usually make little difference in an outcome but sometimes make a world of difference. A rocket with just a bit too little power crashes back to earth while one with just a little more power makes it out of earth's gravitational reach and heads for the stars. A nuclear bomb fizzles or unleashes the power of the sun depending on a tiny differences in timing, material purity and other factors. While it is ridiculous to think that a larger, more powerful cartridge never can or will make a difference. The fact is that, on occasion, they will - just as will using bullet X instead of bullet Y. Or velocity A instead of A+.
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