Pretty much everything has already been said but, one last opinion:
While I would feel more confidence with a 340 Weatherby, 338 Win Mag, or something equivalent, it is also my conviction that any rifle I buy will not just set in the safe. By the time you pay for the rife, a good set of rings/mounts, and a good scope you will have invested the better part of a $1000. I don't want to pay that kind of money then just have it sit in the gun safe, to be used only once every year or two to go after an elk. When it comes to recoil I am kind of a sissy and going to the range and shooting a 200g bullet out of belted magnum is not my idea of fun. One the other hand you could be shooting the 257 at the range and also take it on the occasional coyote hunt. When the moment of truth comes and I am getting ready to pull the trigger on the buck of a lifetime, I would much rather be shooting a familiar rifle that I have been shooting all summer long, rather than one that has sat in the gun safe all that time.
Example: I have cousin that paid over $1800 for a 460 Weatherby. It is a great gun and will kill just about anything on the planet, however he has shot less that 20 rounds through it in the last five years due to the strong recoil, extremely loud muzzle blast, and heavy weight to carryout in the field.