Have owned, handloaded for, and hunted big game a lot with .25-caliber cartridges including the .250-3000 Savage, 257 Roberts, .257 Roberts Ackley Improved, .25-06 and .257 Weatherby Magnum for many years. All will kill game up to elk with the right bullet and bullet placement--and within the range the bullet will expand and penetrate.
While I realize this isn't the minutiae argument the Campfire prefers, this has been my experience with probably 100 big game animals.
Oh, and the .25s also work on varmints...
You forgot in include the excellent, but mostly ignored, 25 WSSM!
Never saw much point in the .25 WSSM, since it's (was?) basically a very short .25-06. Though shot a lot of prairie dogs with one when it was first introduced, during a hunt hosted by Winchester.
But my old friend, fellow gun writer and Montanan John Haviland, has used one considerably--including to take a B&C bighorn ram with the tag he finally drew maybe 12-15 years ago. John's a long-time fan of the .25-06, and was totally convinced it was the best .25 until trying the WSSM.
Not too long after he got the ram, we both went on an "industry" hunt on the King Ranch in South Texas, along with some other folks. The company was USRAC, and the rifles provided were Model 70s in .257 Roberts and .264 Winchester Magnum, and a Browning 1886 in .45-70. I worked up handloads for the .257s and the .45-70, since another "shortage" was occurring and factory ammo was scarce. The .257 load used H4350 and the 115 Nosler Partition, at 2900+ fps.
John had never killed anything with .25s other than the .25-06 and .25 WSSM, and apparently guessed the .257 Roberts wouldn't kill as well. But on the last evening of the hunt I got a shot at a 180-pound feral boar at around 200 yards, during the last few minutes of light. There had been a LOT of recent rain, and the grass was very high. Luckily, the pig was feeding alongside a dirt 2-track, and I managed to get with 200 yards--and had shooting sticks. Instead of trying to get fancy and try for a head or spine shot, I aimed just behind the shoulder and that's where the 115 Partition landed.
The pig collapsed and never moved. John said something like "Wow!" (I did too, silently. Have yet to hunt with any cartridge that always drops 'em right there with broadside lung shots.)
The other nice thing was the boar tasted fine....
