I've got both a .338/06 and a .338Marlin Express. The .338 Marlin is very close to the .338Fed.
I don't think you'll find the recoil any different than a .30/06 with similar weight bullet. ie; a 200gr bullet.
My .338/06 is a bit more gun in that I handload it to top velocities. ie; a 180gr bullet to 3,000fps, a 200gr to 2,800fps and a 250gr to 2,550fps. It correlates closely to a .300winmag for energies.
I've killed two deer so far with the .338Marlin Exp. Both have been bang-flops, the second wasn't even hit in the spine.. about 1" under the spine through both shoulders.
For anything except for the great bears, (and even those with the right bullet), the .338Fed will do anything you can ask of it.
But, for most people, you'll be better off with "just" a .30/06... Adequate likewise with the right bullet. ie: a 200gr Swift A-frame @ 2500fps will probably do anything a .375H&H will.