I just spent a ton of money restocking and rechambering a new model Winchester M-70 Ak from .375 H&H to Weatherby. It was one of the worst mistakes I’ve ever wasted money on. The Weatherby only gives you real world velocity advantage with 300 gr or heavier bullets. You can not get max loads out of fire formed H&H brass due to web thickness at the belt. AND there is a new movement amongst African countries that your ammo must match your rifle. So if your caliber listed and your rifle is marked .375 Wthby DO NOT show up with fire formed H&H brass!
That being said head stamped .375 Weatherby brass is bloody expensive for the menial velocity gains you get for it. I am not a fan.
Now to the point of the OP. The .375 Ruger is a modern non belted efficient case that was designed for smokeless powder and designed to run in a standard length action. The .375 H&H is a long sloping belted case that was designed to run in Nitro Cellulose in a magnum length action in tropical heat. Therefore like all cases designed in that era for that purpose it feeds functions and extracts slicker that owl poop. It is not super efficient by today’s standards. But it still feeds functions and extracts slicker than owl poop and it is plenty efficient enough with modern powders.
If you demystify the reloading manuals the .375 Ruger does exactly what the .375 H&H does but the Ruger does it in a 20” barrel and the H&H needs a 24” barrel to match it. The Ruger only slightly beats the H&H when it is also in a 24” barrel. And all if the data for the Ruger is either 24 or 26” data. Keep that in mind if you are buying one of the 20” Ruger offerings.
If I were building a modern standard length all purpose hunting rifle in .375 I’d probably seriously consider the Ruger. But the H&H is more cooler. So the truth of the matter is I’d most likely build it in H&H anyway. Because more cooler matters.
PS
If you are wondering what I did with that .375Weatherby that I hated? Well I’m glad you asked! Just to upset Robert. I rebarreled it to a horrible .300 Dakota Magnum in a long throated 1 in 11 twist barrel which pushes 180gr bullets at something faster than 3200 FPS and actually does vaporize light game like deer or antelope. Now I hate it too and am back to hunting with my .375H&H. But will most likely use the Dakota when I hunt with Robert just because it’ll be a twist in his britches the whole time.