My go to all purpose hunting rifle is my Browning X Bolt Stainless Stalker in .375 H&H Mag with a Leupold
3-9×40mm VX-1 scope. For deer and smaller game I like to use 220gr or 225gr hand loads. For elk I like the 250gr to 270gr loads and for bear, moose or anything else the 300gr Swift A-Frames.
Alot of people think the recoil is way too much but in all honesty it's better than the punch from a .300 Win Mag as its more of a shove than the punch. Hunters all over the world love the .375 H&H because of the wide range of bullet weights you can get for it. Unlike some cartridges your limited to only a few. The ballistics of the lighter loads almost rival the .30-06 so it is accurate as well.
Some believe the .375 H&H is way too big. However, Hodgon's reloading manual says "some say the .375 Holland and Holland Magnum is our all-time greatest big game cartridge. Others say it's neither fish nor fowl, too big for deer and too little for the really big stuff. But one indisputable fact remains: The .375 H&H will drop a deer with less meat damage than a .270 and has probably accounted for more dangerous game up to the size of Cape Buffalo and Elephant than any other large caliber cartridge.
As fine as the .375 H&H is, it really isn't needed in North America except when hunting the big brown beats at close range. But that certainly doesn't keep quite a large number of moose and elk hunters singing it's praises with each coming season. It's easy to see why. When loaded with a bullet of spitzer form, the .375 H&H shoots suprisingly flat out to 300 yards and delivers a punch matched by few other cartridges.
Until recently, the .375 H&H suffered from lack of bullet variety for handloading, but the reintroduction of the Nosler Partition, the introduction of the Speer African Grand Slam and Barnes X-bullets, and the availability of various custom bullets of controlled expansion has put new life into this old cartridge. When maximum penetration on heavy game such as elephant and cape buffalo is desired, the speer, hornady, Barnes and A-square 300 grain solids are good choices. When shooting elk, moose and the larger African antalope at relatively long range, the Sierra 300 grain Spitzer boattail and the speer 250 grain grand slam are tough to beat. For bone crushing shots on potentially dangerous, thin skinned game like brown bear and African lion, bullets of controlled expansion design are the only choices. They would include the Nosler Partition, the swift A-frame, and the Barnes X-bullet. Two excellent powders for Holland's old cartridge are H4895 and IMR4064."
I've wanted a .375 H&H for 15+ years and was finally able to get one. I will never need to buy another big game hunting rifle as long as I live. Although I probably will end up buying more because I can haha.