Right out of the gate, I'll say that my own opinion matches that of tens of thousands of other shooters (and even some gun writers
):
.416 Rigby is the safer bet if you actually go to Africa.
.416 Remington is fine if you just want to own an 'Uber Magnum'.
Chamber pressure matters, and .416 Rigby was designed to handle the increased pressure from intense African heat. .416 Remington, on the other hand, was just meant to sell rifles by looking good on paper.
My experience includes the following 30 caliber or larger cartridges considered 'harsh', and more...
.300 WM
.300 Wby
.338 WM
.340 Wby
.358 Win
.35 Whelen
.375 H&H
.375 Ruger
.416 Rigby
.458 SOCOM (pussycat)
.458 WM
.450 Nitro 3.25"
.475 Tremor (pussycat)
I have never fired a .416 Remington.
My thoughts on a quick, basic run-down of the cartridges, in my opinion and in the particular rifles that I fired:
The Weatherby cartridges are almost universally more 'punishing' than their 'traditional' counterparts.
.375 H&H lets you know that you just launched a good chunk of lead at the target at a decent velocity, but it's manageable with the correct stock geometry.
.416 Rigby isn't all that bad. ...But I grew up being 'forced' to shoot stuff by recoil junkies, so you learn how to compensate ... or take a scope the the face. Speaking of which, .416 Rigby is the only rifle cartridge responsible for every giving me 'scope eye'. It could have been avoided. The cartridge, in a 10+ lb rifle, isn't that bad.
I actually find .358 Winchester and .35 Whelen to be more 'offensive' in the rifles that I've fired (a Ruger Hawkeye and a custom Marlin XL7), than .375 H&H.
.458 WM is considered by many to be a horribly punishing cartridge. I will agree for top-end loads with light bullets. But with heavy bullets or slightly reduced loads, it's no worse than my .270 (a 10 lb rifle with a hard butt plate!). If you can shoot a 7-lb .30-06 without issue, then you can shoot 30+ rounds of 405+ gr .458 WM loads without feeling it. It's the stereo-typically impossible to describe "hard push" rather than a 'punch' in the shoulder. I once went through 40+ rounds of 'heavy bullet' and 5-6 rounds of 'light bullet/max load' .458 WM in a range session that included several hundred rounds of other rifle cartridges. It was quite an enjoyable day, other than the 'light bullet/max load' .458 WM...
And that brings us to .450 Nitro.
I can shoot it.
I'm willing to do so occasionally.
But I usually avoid it.
With 480 gr bullets, it lets you know that you just ignited a substantial amount of powder behind a heavy bullet, and you might hesitate to pull the trigger again (~12 lb double rifle, I believe) ... but you'll do it.
But when the owner stuffs his 350 gr "pet load" in the double, it's time to just say no to drugs ... err .450 Nitro. Hot loads with light bullets are painful for me to shoot. It 'snaps' my neck like nothing else I've ever fired, and
instantly gives me a headache. I will be the first to say that that particular double rifle does
not fit me very well. Sight alignment is terrible. Length of pull is too short. And it's just ... weird and uncomfortable to shoot.
If I went to Africa for the typical plains game, I'd take my ".243", my .270, and my .35 Whelen. I wouldn't bother with a 'Magnum'. I shoot these rifles better than any of the big stuff, and I'd rather have a well-placed "small caliber" shot than a poorly-placed "large caliber" shot from a ridiculously heavy rifle that I hate hauling around.
A few years ago, my father went on his second trip for African plains game. He ended up taking a pair of .270s, a .300 WM, and his .375 H&H. The .375 H&H never got a chance to play, because the .270s and .300 WM did all the dirty work.