FOR ELK,I VASTLY prefer the over thirty caliber cartridges throwing at least a 225 grs and I prefer the 250-270 grain weights in the 338-358 and 375 calibers launched at a minimum of 2300fps. thats a preferance gained after watching close to a hundred dead ELK dressed out over 35 plus years in several states and having hunted in several larger ELK camps (lets say IM an OBSESSED ELK HUNTER)and having looked at the internal damaged carefully. now that being said and having hunted with guys over the years carrying 25/06 and 257 wby rifles on several occasions and having one guys dad carry a 257 roberts for many years I can honestly tell you that the guy BEHIND the rifle has a great deal to do with what works well!
will a 257 roberts, or 25/06 , KILL ELK? HELL YES!, in the hands of an excellent shot its fully up to the task under most conditions if premium bullets are used. and the range is not excessive. but it does not have the same effect on impact, it doesn,t penetrate as deeply from less than ideal angles, and it won,t leave the same wound path thru an ELK.
now why would you put yourself under a handicap, that will limit your range, limit your potential choice of shot angles , when a differant sellection that won,t have those potential problems, is available. like the others Id suggest a 270 win as a more reasonable minimum
I started out with a 30/06, it killed ELK just fine but it had no where near the instant effect on impact the 338-358-375 calibers had, nor did it tend to leave exit wounds on raking angles