I recently went through this debate. There are pros and cons to both. I ended up with a 375 Ruger for the following reasons:
1. More production rifles at a reasonable price available thanks to Ruger. I bought a Ruger Hawkeye FTW 375 Ruger. Vx3i 3.5-10 scope in Spuhr rings, silencerco muzzle brake and silencerco Hybrid. Toying with the idea of chopping it to 18.5" but want to see how it balances and shoots as is first.
2. Its simply a better case design. I'm not sure how anyone without bias could argue this. Shorter to fit in a shorter lighter action. More case capacity for 100fps more even in shorter barrels than the H&H. Removal of the stupid belt that is obsolete on modern firearms.
3. Same or greater ballistics in a shorter barrel. Shorter barrels are very handy for a brush gun or in places like Africa especially if you want to shoot with a suppressor.
4. Good factory ammo from Hornady and I hear they are doing a run of brass in June you can stockpile up on.
5. The 375 is inherently a more accurate cartridge (This is conjecture from many wiser than I)
The only disadvantages are 1 less round in the magazine. Factory ammo availability, but if you reload it's a moot point really. Those are the only ones I can really think of, so for me the pros for the Ruger outweighed it's cons. Perhaps one could say the H&H may feed more reliably, but I have not read of a single complaint of a 375 Ruger not feeding reliably so I did not consider this in my comparison because from my research they seem equally reliable in quality modern rifles.
Holding on to a caliber because of nostalgia is fine, but don't sit and act like it's a better cartridge by design because it is objectively not all other things equal.