Gearchecker, the .338 will probably produce more felt recoil than your .375. I think this is largely due to the smaller case mouth relative to the case diameter--one of my gunsmiths calls it the "jet effect." I don't think it'll be a lot more, and it sounds like you are not recoil sensitive. My Model 70 .338 WM kicked a good bit harder than my Whitworth .375 H%H does.