Like said above a 308 with the same weight bullet will have roughly the same recoil.

No big deal really.

That said the 338 fed is more efficient than a 308 due to the piston effect, IE larger diam bullet.

I have a 19" barreled 338/284. Slightly ahead of the 338 fed, but not by a mile or anything.
Recoil is stout with heavier bullets, but more so because of the 19" barrel than anything else.
When I went from 24" to 19" the jump increased a lot.
Still very manageable though.

It will DRT a pig like you would not believe with barnes bullets.
I have been using mostly 210 gr tipped TSX bullets, but even a 160 TTSX would TKO a hog right on the spot.

A 338 TTSX round will open up to about .67" and thats a big hole.

Its a good round.
Midwayusa sells 338 fed A+B barrels for like $130. I reamed one and chopped it to make my 338/284 barrel.