While the P.O. Ackley link adds value and interest (at least for me), I'd still stick with the .257 AI just for what it is.
In my opinion, .257 Weatherby is not going to give you the added "horsepower" that you're looking for, for elk. More velocity? Yes. Better performance? That's a matter of perspective. (And my perspective says sees a 'no'.)
If you like long throats that compromise accuracy, more meat damage, more explodey impacts, and more disappointment, then .257 Wby is the cartridge for you.
But if you value quick, clean kills and a more forgiving and predictable cartridge, .257 AI is the winner.
If you want 'more horsepower', step up to a larger caliber.
(While I admit that I don't have hands-on experience with .257 AI, I do have experience with similar cartridges; and I do have experience with .257 Wby. The 'Magnum' quarter-bore is not all it's cracked up to be.)
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Sidebar:
About two months ago, my father called me to talk about rebarreling an heirloom sporterized Springfield 1903A3 that was built/customized by his father (my grandfather) in the late '50s and is the single most sought-after firearm that my grandfather passed down. My father, for whatever reason, suddenly decided that .30-06 wasn't good enough any more, and he "needed" that rifle to be .30-06 AI.
After wading through the mess of arguments put forth, I realized what was going on and told him flat out:
"Dad, you haven't shot a big game animal in six years, and you're bored. Since you can't fill tags, you're looking for excuses. You've gone through at least two new hunting rifles per year for eight years, now; and you've gotten sucked into 'magnumitis'. You need to go play with the grandkids' barbies until you realize what your motivations are..."
About three days later, he called me back:
"[FrankenMauser], I did some thinking and you're at least mostly right. So... ...what if I went .338-06 instead?"
"Alright, dad. That's at least worth the trouble. I'll find you a deal on a good barrel blank..."