DK - I son't know why guys like Pioneer try to condem new cartridges. I bet he owns a .338 and he probably loves it. It IS a great cartridge and like he said, a proven one. But with the newer propellants being designed you can get equal performance from smaller cases than in the past. That, and the firearms/ammo companies do develop new cartridges sometimes jus to boost sales. Look at the 30 T/C. Another similar 308 sized cartridge.
Anyway, as for your question, I know the 338 recoils more than the 300 Win Mag which I had and my 325WSM recoils about the same as my 300 Win Mag did. And my 325 is in a much lighter Browning Micro Hunter as opposed to the heavy Ruger 77 in 300 Win Mag. So all othere things being equal, I would say the 338 kicks more than the 325. But each rifle has a different felt recoil. Even rifles of the same model and cal. Some things you can do to change reduce felt recoil is to put a recoil reducer on your rifle or a different butt pad like one from limbsaver.
Remember, felt recoil is different than actual recoil. Actual recoil is a law of physics and can't be changed. Felt recoil can be altered by stock design, recoil pads, etc.