Very noticeable. I have 2 458s, a 375 H&H, 9.3x74R and a 338LM.
The 416 is a sharper recoil in my CZ550 416 than in either of my 458s (CZ550 and Winchester Model 70). The 375 is a full step down in recoil on my CZ550 375 H&H. It may be the shoulder saver on my 338LM, but the 375 and 338 feel quite similar, notwithstanding the extra 1000 ft-lbs on the 338.