The .257 Roberts, as well as the .244/6mm Remington, are based on the 7x57mm Mauser cartridge case and is a flat-shooting round with most bullets suited for the round and is well-suited for antelope and deer, but a bit "light" for elk and moose in most situations.
The Remington Model 722 has a 1:10 twist barrel which should handle even the heaviest 115 to 120 grain bullets available in .257 inch diameter, so the heaviest bullet isn't a problem. However, the normal magazine length in a Remington 722 can only handle cartridge lengths up to 2.75 inches unless it is modified which usually means the heavier .257 bullets must be seated more deeply in the cartridge case than is needed for best accuracy performance, even if the chamber has a long, deeper throat needed for best accuracy.
Because the Roberts is based on the 7x57mm Mauser cartridge case, the action needed for the .257 Roberts should be a tad longer than the regular short Remington 722 action. Of course, that problem goes away if you have a custom-altered Model 722 with a slightly longer magazine and a long chamber throat to accommodate the longer, heavier bullets (115-120 grain) seated out to their longest length for best accuracy if you use 'em.
However, if the rifle which you are considering can handle a .257 Roberts cartridge with the heaviest bullets like the 115 or 120 grain Nosler Partition Bullet set out at normal length through both the rifle's magazine and chamber's longer throat, then it's a great buy for fine accuracy and even the largest deer.
While Ned Robert's little package is "dynamite" with lighter bullets like those in the 87 grain bullet weights with muzzle velocities in the 3,100 to 3300 fps range using maximum "book" loads of IMR3031 and IMR4064 and the 100 grain bullets still have a "hefty" muzzle velocity in the 2900 fps to almost 3,000 fps range with maximum loads of IMR3031, IMR4064 or BL-C(2), the heavier 115 grain to 120 grain bullet's muzzle velocity drops off drastically... down to the 2600-2700 fps range at best.
And so, for best performance, the 100 grain bullet is about the heaviest bullet that maintains the reasonably high muzzle velocity required for maximum bullet energy delivered to the game together with very good flat-shooting characteristics and fine accuracy.
While there are higher-velocity, flatter-shooting examples of the .257 caliber (the .25/06 or .257 Weatherby Magnum), the "mystic" of the .257 Roberts can't be denied.
Strength & Honor...
Ron T.