I agree that with factory ammo only, the 308win is probably much more available in most of the US. And the 308, with it's 51mm long case works in short actions.
Loaded to comparable velocities with similar bullet weights and rifle weights, the felt recoil should be about the same.
If you are, or want to be a hand loader, the 7x57mm Mauser really shines. US ammo is downloaded due to the possibility of being used in a weak small ring Mauser action (m-1893s and 1895s, plus old Remington Rolling Blocks)
If you use a stronger M98 type action, a M-70win, a M-700 rem, Ruger M77, CZ, or Tikka. Then you can safely hot rod the 7x57mm
With the 7x57 you can push a 140 grain bullet at over 2,800 fps from a 22 inch barrel. (example 52 grains of RL-19 and a 140 grain Nosler partition loaded in a Ruger No. 1 zips out the 22in barrel at 2,844 fps.)
51 grains of RL-19 will push a 150 grain Nosler ballistic tip at 2,780 from the same barrel.
And I use 48.1 gr of IMR-4831 to push a 160 grain Sierra Game King from my 20 inch custom Mauser barrel at 2,600 and that is not top top pressure, just super accurate.
For the 308 you can push a 147-150 grain bullet at 2,700 to 2,800 fps from a 22 inch barrel, and 165s to 2600-2,700 fps.
The 308 has a slightly larger frontal mass and you do have the option of going to a 180 grain bullet in factory loads and maybe even a 200gr in hand loads.
The 7x57 has a slightly longer case neck which is better for hand loading long boat tails, but not all commercial rifles have the rifling twist or chamber to handle long-loaded 7mm boat-tails.
