This is really just a permutation of
@mcb's thread on "minimum cartridge for deer."
I can say, a specified limit of kinetic energy isn't the best metric for the minimum cartridge limit. It might not be the WORST metric, but I can think of few metrics worse than KE. None of the available calculated metrics are without bias (I'm pretty sure I have a post on here somewhere which outlines the biases of each of a dozen or so common metrics for stopping power). Any time you have a dependency upon speed AND mass, you're opening the door for imbalances where singular metrics don't tell the whole story. This is how we end up with the absurdist arguments such the Taylor KO Factor is bunk because a baseball pitch has 4x higher number than a 45-70 (TKO values diameter as much as speed or mass), or such the 243win has as much KE as a 45-70 (because KE values speed over mass)...
And of course, any of these metrics are typically based around exactly those two parameters - speed and mass, the product of which is momentum... momentum likely has more merit than most metrics, since we're dealing with real world, inelastic collisions, where momentum, but NOT kinetic energy is conserved. But the transfer impulse, shot placement, inefficient losses due to fragmentation, and dumb F'ing luck (or lack thereof) are all extremely influential variables...
I laugh whenever I see 1,000ft.lbs. touted as the minimum KE requirement for deer. 1,300ft.lbs. is even moreso laughable. .357mags will drop deer very well at 50yrds, leaving the muzzle with only around 550ft.lbs. As noted above, arrows kill deer every year with less than 60ft.lbs. at the bow, let alone upon impact. Alternatively, I can push a 40grn 20cal pill in 204Ruger to about 1,300ft.lbs. but only hit about 900-1000fps with a 240grn bullet in 44mag. - would anyone suggest a 204Ruger is a better choice for whitetails at 100yrds than a 44mag?
It's all physics - comparisons of the CORRECT metrics can aptly describe disparate samples along the spectrum of cartridges, but using KE alone, or really any of the common metrics used in the sporting arms industry alone, is a fool's errand.