Most 7X57 mauser's were of the '95 version, which arnt as strong as the 98s.
Taking that in mind, factory loads are produced assuming they will be shot in the 95s so are loaded accordingly.
I really don't see the 7X57 having less recoil then the 270, but to be honest I haven't shot many factory 7X57 shells.
I love my 257 Roberts, but I believe it might be on the light side for elk.
My go to elk rifle is a Model 70 Featherweight in 270. I don't find the recoil objectionable. And I will admit, Im a wimp when it comes to recoil.
My wife cant handle recoil very well. She broke her back and has three rods between her shoulder blades.
Yet she can handle the 270 with out undo discomfort. Granted she cant shoot 20 + rounds at a session but if you need that much ammo hunting, no rifle is going to work for you.
The 06 is an excellent round, as in the 308. Neither are known as hard kickers but they do produce a tad bit more recoil then the 270.
Most of my 06s are military surplus rifles (Garand, 1903a3 & a4, & Model 1917). They have steel buttplates. They will get you after a while unless you use a heavy shooting coat (which I use). But again, you wont notice the recoil while shooting at elk.
The deal is, sight in and practice in comfort because youll be shooting more ammo. There are several devices to use. I like the shoulder pad put out by buffaloarms.com. It absorbs the recoil of my 375 H&H quite well, making it a pleasure to shoot.
I don't use the pad while hunting and Ive never noticed recoil while shooting at game.
The problem comes is shooting heavy kickers in practice and developing a flinch which will carry over to hunting.
Regardless of what rifle/ammo check out this shoulder pad, IT WORKS.
http://www.buffaloarms.com/Shoulder_Recoil_Pad_it-160522.aspx?CAT=4019
Shooting is suppose to be fun, getting beat to death isn't fun.
Regardless what you shoot, this shoulder recoil pad puts the fun back into shooting. Its comfortable and IT WORKS. I can shoot my steel butt plate M1903a3 all day while wearing mine.