Bumppo: I think between the two (260 Remington & 257 Roberts) I would go with the 260 Remington these days.
I have harvested Antelope (about 80 of them to date) with about every standard caliber from 22-250 Remington on up through 300 Winchester Magnum.
But the 260 Remington is just exactly what the Doctor ordered when it comes to mild recoil, excellent accuracy, superb lethality (on Antelope and Deer!) and impressive ballistic (trajectory) performance.
I have killed Antelope out to just past 500 yards with my Remington 700 VLS in 260 Remington using the wonderful Nosler 100 grain Ballistic Tip bullets and a Leupold 6.5x20 variable scope!
I have used the 257 Roberts on Antelope and it will get the job done but the nod here goes to the 260 Remington.
Best of luck with whichever you choose.
Hold into the wind
VarmintGuy