Noted Whitetail biologist Dr. James C. Kroll sets the criteria thus:
1-A bullet weighting at least 140 grains.
2-Velocity approx. 3,000 fps.
He considers the 257 marginal but acceptible.
I believe he uses a 7 mm magnum, 140 gr. bullet.
There is no bigger fan of the 7 mag than me...that said,I'm sure he knows what he likes....but his criteria excludes things like a 270 Win,the 7x57 and 7/08,the 6.5x55,and many loads,both factory and handloads, for the 280 Remington;as well as the 257 and 25/06.
Need I say more?
As to the 308 and 257,a rifleman will get it done with either one.