I own and shoot on a regular basis both in various chamberings and actions. They include six 375's four in 375 H&H, one 375 Ruger, and one 375/338. I also have six 416's, four 416 Rem Mag, one 416 Ruger and one 416 Taylor.
I built them all myself and feel comfortable with all, and wouldn't trade or sell any of them, although I will soon start to pass some to Sons, grandsons, and granddaughters.
I started building them in the '80's and already gave a favorite 375 H&H ( a seventh 375) to one of my sons who took a Moose with it.
Three of my 375's and two of the 416's have all been to Africa and taken game from Buffalo, to Leopard and many plains game. They all also get a workout on everything here in Colorado and Wyo. from Antelope to elk........still trying to draw the Moose Lisc.
I have tried and used many various bullets and powders in my loads, but have settled on the Barnes, TSX as my hands down favorite. I still use both Noslers Part. and Nosler solids, Swift A Frames, Hornady's, softs and solids ( really FMJ), and even some Fusions bought a few years ago from "pull downs".
But when the money is on the table it is the TSX, and Barnes Banded Solids period.
Powders include, W760, 4350 AA2700, H380, and RE15 Varget, and AA2520 in the 416 Taylor, as having giving good results. W760 is hands down the best for the 375 H&H. And AA2700 and H380 in the 416 Rem.
The 416 does give you that power edge. However when I really want power I reach for the 458 Win Mag and 458 Lott.
I have just finished a 500 Jeffery that I hope to use on Elephant next year. One of the 416's or one of the 458's will go along as the overlap and "light" rifle.
I have found that in both the 375's and the 416's regardless of the chamber configuration it is the load and bullet choice that really makes for the successful hunt.
In the end I suppose there is a reason the 375 H&H has been around since 1912.........It just works great all the time if there is proper bullet placement. If you want true versatility you can't go wrong with the 375 H&H.
A 375 H&H is like a good well trained Lab, it just wants to please you and it won't let you down.
If it is going to be just one rifle you won't be disappointed with a good 24" barreled 375 H&H.