I'm a long time shooter, but have not hunted much. Mostly pistols, big bore pistols, which force you to handle recoil if you want to hit anything. I do have and like to shoot rifles as well. Among my rifles are 4 Weatherby Mark Vs, a 375 Safari Custom, a 340, a 300 (my fathers), and a 30-06. My first shot with the 300 was about 55 years ago, standing, at a rock about 350 yds away, about 2ft x 1.5 feet, in front of my Dad. I was nervous. Holding slightly high, I did break the rock, though the unexpectedly fast recoil lifted the rifle briefly out of my hands. Later, I learned to hold onto it a little better. I suppose this shot shows the 300 Mk V at its best, higher long range impact velocity and energy. It didn't hurt to shoot this rifle, it just had a surpisingly rapid recoil.
The 340 I haven't yet shot much, having just bought it. With reasonable handloads and a 200 Speer HotCor, it's very comfortable to shoot, not really different than the 300. I just got some 250's to play with, and expect more recoil from them, but less recoil impulse. For a general purpose rifle outside of buffalo and elephant country, it's about perfect, to me. Covers both end of things for NA very well.
The 375 Safari Custom is a superb and beautiful rifle, very nice wood. With the Weatherby factory loads, 300 gr Nosler Partition at 2800 fps (nominal), it does hurt the shoulder a little bit, so I limit the number of rounds I fire at a setting. Cost is also a factor with this round. The most excellent point is that it can be loaded down to 375 Ruger and to 375 H&H velocities, and is then very comfortable to shoot. So, if your really need the long range impact velocity and energy, the 375 Wby is a pretty good cartridge. If you are in a hunting situation, by all means load to the least necessary level. Or, just drop in some 375 H&Hs, which seem to function well in the rifle. It is heavy, about 11 lbs. For me, this is too heavy for a DGR, which needs to handle nimbly, damn the recoil. Same comment on my Ruger 458 Lott.
I've not shot the 30-06 yet, due to Covid19, but it handles very nicely, with a 24" bbl.
The low bolt lift is a great asset. So is the smooth action. I'm not particular happy with the Weatherby stock's appearance, though it does have some appeal, but I find it a very comfortable and effective stock to shoot and it comes to the shoulder well and quickly.
My father taught me when I was 10 years old to jam the bolt at both ends, to ensure complete cycling; this habit ensures the reliability of both push feed and CRF actions. The habit allows the full advantage of the low bolt lift of this action. So I'm having a custom rifle built on a Mk V action in 458 Lott, composite stock, with hi-vis fiber optic iron sights, to weigh ~ 8 to 8.5 lbs prior to scope.
There is no doubt that recoil will be vicious in this rifle with full house 500 gr of 550 gr bullets. But I'll mostly shoot 350's loaded to 2600-2700 or so, which is a much tamer beast. If a circus elephant goes mad here in town, I'll just take the scope off, load some 500s, and get fairly close. If I get the elephant, I think the city will probably pay to have my unconscious body trucked back in from the next county. That said, there is a notable lack of wild elephants in my neighborhood, due no doubt to the presence of my elephant rifles and my own eternal vigilance.
I've always wondered about the 378, the 416, and the 460. These are very special purpose cartridges. I've chosen to save myself the trouble, and avoid them. You can practice and learn to control the rifle even with these rounds, but no real point unless you are a PH and need the big boom for backup. Even then, I'd probably pick a 500 Jeffery or 505 Gibbs or a 500 NE, to avoid that vicious recoil impulse. The recoil with these old cartridges is still very substantial. IF the 450 NE was effective for hunting, then so are the 458 WM and the 458 Lott.
So, my 2 cents on Weatherbys. Good rifles, some good cartridges which do extend effective range, despite Mr. C. Hawkes' MEPB range concept. He should also remember that 30 extra yds is 30 extra yds, and that energy at impact deserves consideration.
Pooh-poohing others choice of gun & cartridge is an arrogant exercise. Weatherby's as good as anything else, when properly applied - a pro-viso that applies to all rifle cartridge combinations. A good PH may fear his client, but shouldn't, without reason, fear his choice of rifle and cartridge. Also, the world being what it is, a PH needs to focus on teaching the ignorant, and saving those resistant to his teaching.