I don't know about "knockdown" power but in my experience a deer shot with the .270 falls down faster than one shot with the .243. I've shot quite a few with both calibers, they go down faster with the bigger bullet. Note the .243 goes a couple hundred fps faster than the .270.
With a handgun, I don't know. I do know that on steel plates the .45 will knock the plate down way more forcefully than a .38 or 9 mm but that's not the same as in soft tissue. More damage from a larger bullet would cause more bleeding tho.
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