I remember an incident thirty years ago. I was sitting down and shooting a warthog with a 300 grain original Barnes .338". The pig dropped at the shot, apparently without the spine being touched. But a thought crossed my mind--hey, that was different, a little more 'umph'. It seems that I noticed a difference from the normal 250 grainers that we were shooting. Probably the difference was more from sitting, though, since I was most often leaning against a tree with my hand protected by my hat.
I wouldn't think twice about recoil in the 375, just learn to shoot it and get plenty of dry firing so that you know what a good 'sight-picture' looks like.
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"A well-rounded hunting battery might include: 500 AccRel Nyati, 416 Rigby or 416 Ruger, 375Ruger or 338WM, 308 or 270, 243, 223" -- Conserving creation, hunting the harvest.
If you can handle the recoil from one the other will be a negligible change, sometimes the 300gr seems a bit less because of lowered velocity. Thanks, Lynn