I’ve got a couple of my late fathers model 70’s, one in 338 win and one in 375 h&h. I’d rather shoot the 375, it’s more of a push than a punch, but that’s just me. I haven’t carried the 338 in 9 years. That didn’t help your decision at all, but I feel obligated to share a story.
One of the worst kicking 338WMs I ever worked with was an early '80s Mod 70. It was on sale at Carter's Country, in Houston. I told a friend about it, he bought it, wanted me to load for it. I had only worked with the 7mm Rem mag, all the rest were 30-06 and smaller. He bought the dies. etc and I set him up with two loads. The Sierra 250 BT and the Speer 200 HC. They were both book max, but I can't remember what powder I used, probably IMR 4350. Anyhow, it beat the dog snot out of me! He killed a Texas whitetail with the 200HC, said it took a big chunk out of the offside, but he didn't care. He was a little skinny kid, I am much bigger, ha. My FIL had a 70's make of a Mod 70 Clone made for Sears, the "Ted Williams" 30-06 that was also a pile driver, ouch! Bad stock design for my body shape, ha. In early 90's I bought a Winchester 70 Safari Express in 375 and it too was just a nice push! Heavy as a truck axle for Utah's elk mountains, wow!
P.S. My first 338WM was a couple years earlier than the Win 70 375, it was a MarkII and had a pretty stiff trigger. It shot the then available Remington Factory load that that the 250 GS bullet into dime sized, 3 shot groups! It kicked the Burris 3x9's reticle out my first range session. They replaced it with a factory repaired Leupold 2.5x8 , one of my favorites. I made one unfruitful week long elk hunt with it and it was a joy to carry in the field (for a 40yrs old!) The following year right before elk season, I took it to an inhouse gunsmith at a local sports store. I wanted him to smooth up the trigger. He did smooth the trigger a tiny bit but I assumed he would have used a little strength to tighten action screws, but ( shame on me) I didn't check for myself if the receiver screws were tight. I tried to blame my long work days, but no excuse. ha It broke its bedding and I had to settle for a club like Choate synthetic, made my rifle close to 10#. Yeah the added weight made the recoil better (though it wasn't bad with that Ruger style stock.) I traded that rifle in on my first Mod 700 Mountain Rifle in .280 ( which I had Ackleyed by a different gunsmith.) I have since had an older Mod 77 "Tanger" that did not shoot for beans, but that Mark II was nice! If I was just a Road Hunter or hunted hayfields, sure, a heavy 338WM is awesome to have, settles right down in the High Prairie winds. But for hunting the rain soaked knife ridges, up above Schofield Reservoir, no, they are heart attacks just waiting to happen, ha