RIPP, Allenday & John have hit it spot on.

To slight the .416 Remington because of "high pressures" is to make a mountain out of a theoretical molehill.

Going the other way, a theoretical case could legitimately be made that factory loads or factory-pressured handloads in the .416 Rigby would make it a hazardous choice for cold weather hunting due to the theoretical possibility of misfires or hangfires. This might be more likely to occur than overpressure loads in the Rem .416. But just as the .416 Rem can be loaded down a smidge, the big Rigby can be loaded up.

Based on this argument, a guy should leave his .30-06 or .300 Win Mag home as it might blow up if he takes it to "Africa".

Both .416's are great cartridges for Africa from all I've read and heard.

Also, hunting with a "max safe" handload is generally a poor idea wherever a guy hunts IMO. Some guys do of course but not me. I always load down. Maybe we are dealing with handloading semantics here, but I attempt to load all my handloads to notably sub-max pressures and I try to test them all in the summer. It IS a good idea to test one's handloads and factory ammo in similar conditions to which they will be used in the field, hot or cold. If there is time to plan, this should be part of it.

But most places where hunting takes place in Africa isn't any hotter than much of the summer in most of the lower-48 USA. The "heat" of subsaharan Africa has been so overblown in my opinion. Testing can occur here.

My neighbor RIPP over in Montana can test his loads during the summer there and duplicate African heat {or exceed it}. Granted, he better hustle as has only 3 weeks of summer to get the job done {his summer is about one week longer than mine...

} but it already sounds like he works it in so he doesn't have any problems.

Seriously, it is a good idea to test max handloads. Problems CAN occur. Last year the little thermometer showed 140 + degrees on the shooting deck on the back of my Polaris Ranger and I began to blow primers in some of the .223 squirrel loads I worked up in winter but hadn't tested in the heat of summer due to my own impatience. In the mornings all was well {very chilly} but at the heat of the day they blew {in this case, the bullets were just touching the rifling}. Also the gun was untouchable due to the heat {in spite of being painted which makes it "cooler" in severe heat} and the ammo had to be carried in my pocket to cool it off. Last year we had three days in a row where there was hard frost in the morning and the high for the day was in excess of 100*F. If that ain't Namib or Saharan conditions I don't know what is!

There's nothing inherently wrong with either of the cartridges. Attention to normal handloading procedures should mitigate against any trouble from either.