No experience with the 257, hunted with 2 25's this year on 4 animals. 2 goat and 2 deer, worked well out past 400 and if either recoils more than my 243 I would need instruments to measure it. This was with a pre accutrigger savage and a savage edge. The edge kicks a little bit more, but I replaced the pad on the other savage with a nice squishy one, so not apples to apples.
Going off of others math the 257 has about an additional 20 yards on it's PBR using 115gr bullets. I plan on continuing with the 25 for deer sized game. I'd use it for coyote hunting but I just picked up a stevens 223 specifically for that.