The .264 and .257 WTBY are big kickers compared to the .257 Roberts. I would equate the "Bob" in equality of recoil to a heavy loaded .243 or 6mm Rem., not much difference.

With good 100gr. bullets, ie: Partitions will do, the .257 will make about 3,100fps to 3,150fps. That is about the same ballistics as a maxed out 6mm Rem. Anything from 2,900fps to that range will work fine on most everything.

I used that bullet in my .257AckImp, but at 3,480fps, on a moose, side head shot, exited out the off-side ear, perfect 1" hole in the cartilage. Since that was a 40yard shot in the bush, most anything making the same shot would have worked, even a .222 with a 45gr. TSX., but goes to show, more than the easier shooting rifles is not normally needed. The next fall's deer at 80yards, same load, poleaxed - "dead right there". The old "BOB" would have done the same, even with a low-ball factory load. After those two years using it, I swore to get a standard Bob if I went .25 cal again.
Sold the AckIMp. 257 to a friend who 'needed' it, then years later, bought a .25/06 as it was a good price. Shot it a bit, too much for that bore size, so sold it the next year., dies, brass and all for a loss, just to get rid of it.
I then bought a .243 (couple) - NOW, I'm happy, but would have been happier, with a .257 Roberts - maybe I should re-barrel?