Apples & oranges?
The question is "What hits harder?" and the response proposes to use energy as a unit of measure "Both develop about the same muzzle energy, somewhere around 5,000 lb./ft."
This is not the direction I would go...
In the calculation of energy:
- velocity is squared;
- mass (i.e. weight in everyday language) is not;
- frontal area (i.e. caliber) is not a factor included in the equation.
These are the reasons why high velocity small or mid calibers make up in energy over larger calibers shooting heavier slugs at lower speed.
Using Swift factory data for both cartridges, so that reloads variations are mostly taken out of the discussion, the .416 Rigby 400 gr has a 288 fps initial velocity advantage over the .458 Win 500 gr. This gives the .416 Rigby a muzzle energy of 5,249 over the .458 Win's 5,100.
Going by energy alone, the .416 Rigby 400 gr hits ~3% harder than the .458 Win 500 gr...
For comparison, still going by energy alone, the .458 Lott 500 gr hits ~4% harder than the .416 Rigby 400 gr, and ~7% harder than the .458 Win 500 gr...
I own a .458 Lott, I too in the innocent pre-chronograph days was convinced that it outperformed the .458 Win by grand leaps and fantastic bounds, but as hinted by
Badboymelvin, the DATA shows otherwise. ~7% additional energy is hardly worth writing home about, especially (see here under) if the price to pay for ~7% higher energy is ~27% more recoil...
There is a large body of experience in the hunting world going back a century that challenges the use of kinetic energy alone as an adequate measure of how "hard" a bullet "hits"...
One with considerable experience who took the pain to design a better answer was "Pondoro" John Taylor. He designed a formula to calculate what he called the Knock Out Value (KO value).
This table is copied from Taylor's book
African Rifles and Cartridges:
The table does not show the .458 Win (introduced in 1956) because it did not exist at the time the book was written (1948), but since the .458 Win 500 gr load was designed to duplicate the .470 NE 500 gr load in both velocity and energy, we can approximate an answer using the .470 NE 500 gr data. The only .416 in existence in 1948 was the Rigby, so the .416 data shown in the table is the one we are interested in.
The KO value for the .470 NE 500 gr / .458 Win 500 gr is 71.3
The KO value for the .416 Rigby 410 gr is 57.25
Using Taylor's KO value, the .458 Win 500 gr hits ~25% harder then the .416 Rigby 400 gr.
Taylor's comment "
suffice it to say that the final figures agree in an altogether remarkable way with the actual performance of the rifles under practical hunting conditions" are good enough for me. Personal choices of life set aside, it will be a looooong time before I challenge Taylor's expertise and experience hunting dangerous African game...
Recoil
A 10 lbs .416 Rigby rifle shooting a 400 gr bullet at 2,400 fps generates 58 ft/lbs of free recoil.
A 10 lbs .458 Win rifle shooting a 500 gr bullet at 2,100 fps generates 55 ft/lbs of free recoil.
(For comparison, a 10 lbs .458 Lott rifle shooting a 500 gr bullet at 2,300 fps generates 70 ft/lbs of free recoil.)
I hope this was of interest