Alcornoque,
.458 Winchester Magnum is a fine choice for dangerous game hunting in Africa, has had been a tried & tested caliber since 1956.
The cartridge case is based on the .375 H&H case shortened to 2.5 in (64 mm), and "blown out" (case opening enlarged) to accept a bullet of .458 in (11.6 mm) diameter. The cartridge headspaces on the belt. The developers of the .458 Winchester Magnum sought to duplicate the ballistics of the 450 and .470 Nitro Express in a cartridge that would fit in a standard bolt-action rifle. With good handloads one can expect approximately 2,170 ft/s (660 m/s) using 500-grain (32 g) bullets (achieved using a barrel 24 in (610 mm) in length). Though somewhat overpowered for North American game like deer and elk, the .458 is most useful for African game like Cape buffalo and lions. The 458 Winchester Magnum is the largest of a family of "short magnums" that include the .338 Winchester Magnum, .264 Winchester Magnum and later the .300 Winchester Magnum.
Winchester currently offers ammunition in the traditional 510 gr (33 g) Soft Point and the new 500 gr (32 g) Nosler Partition and Nosler Solid. The Winchester 500 gr (32 g) loading has a muzzle velocity of 2,240 ft/s (680 m/s) and muzzle energy of 5,570 foot-pounds force (7,550 J). Hornady offers what they call a "heavy magnum" loading that features a 500 gr (32 g) bullet with a velocity of approx 2,260 ft/s (690 m/s). They use a special double-based cooler burning propellant ("powder") not available to the public for handloading. This innovative loading allows the .458 Winchester Magnum to attain 5,670 foot-pounds force (7,690 J) of muzzle energy. Federal Cartridge is now loading a 500-grain (32 g) Barnes X bullet with a sectional density and ballistic coefficient that allows it to maintain approximately 2,000 foot-pounds force (2,700 J) of energy at 500 yards (460 m) and a flatter trajectory that has never been attained with this cartridge and bullet weight. Numerous companies offer rifles in this caliber, including the Winchester Model 70.
The rounds for the .458 Win mag are more expensive than cartridges like the popular .30-06, making handloading a worthwhile effort. Though more expensive than deer hunting ammunition, the .458 Winchester Magnum is significantly less expensive than its competitors. For many decades the .458 has been the most popular rifle cartridge of professional hunters who pursue heavy dangerous game in Africa because of its performance, price, and availability. When British ammunition companies, including Kynoch, began closing in the 1960s, Winchester and the .458 Winchester Magnum filled the gap left behind.
The recoil of the factory loads is about 70 foot pounds. Handloads can be made that will make this cartridge more comfortable to shoot.
The .416 Rigby or 10.6x74mm was designed in 1911 by John Rigby & Company of London, England as a dangerous game cartridge and is the first one to use a bullet with a diameter of .416". The rifles, as built by John Rigby & Co., were initially made up on Original Magnum Mauser actions although in later years, some were made on standard length actions, a perfect example being the rifle used by legendary professional hunter Harry Selby. Other famous users of the cartridge were Commander David Enderby Blunt, John Taylor and Jack O'Connor.
The cartridge case is one of the largest ever designed for a bolt action rifle and the huge case capacity allowed for good performance without creating excessive chamber pressure. The cartridge was originally loaded with Cordite, a powder that resembles long spaghetti strands that burns very hot and is sensitive to changes in ambient temperature. Like many cartridges designed by the British in this era, most of its intended use would have been in the hot climates of Africa and India. Large increases in chamber pressure often resulted under such conditions, sometimes making it difficult to extract fired cartridges, something that would be virtually impossible with the .416 Rigby.
Most .416 Rigby factory-loaded ammunition propels a 400 grain bullet in the neighborhood of 2,300 ft/s (700 m/s). Additionally, it doesn't have the tremendous recoil of other large cartridges such as the .460 Weatherby Magnum. Recently-offered lighter-weight bullets, affordable reloading brass, and reasonably priced American and imported rifles have made this caliber increasingly popular for hunting large game in the United States.
Until recently, the use of .416 cartridges was mostly confined to Africa, where they were used primarily on dangerous or "thick-skinned" large game such as rhino, elephant and Cape buffalo.
The description stated above is about the pros & cons of both the rifles, you have be the best judge.
Happy Purchasing one of these immaculate calibers.......
Monish