Something that other have eluded to, but not said outright is that muzzle brakes redirect pressure, and this is how they reduce recoil. The same pressure that pushes on the base of the bullet to drive it out of the barrel, is the same pressure that is forced against some form of restrictor plate in the muzzle brake to push it (the muzzle brake) away from the shooter. This redirects the sound and pressure wave to the side, or possibly back towards the shooter and bystanders.
As I like to put it, muzzle brakes do a fantastic job of turning recoil into noise.
Don't get me wrong here, as i have muzzle brakes on all manner of rifles, pistols and shotguns, but those are RANGE firearms that I usually have earplugs and headphones on when shooting in competition. I NEVER have any kind of brake on a hunting gun.
Most of us here debate on how much power is needed for .458 dia 500 grain bullet to do it's job on African Dangerous Game, and 2200-2400 fps seems to be the mark. Anything beyond that doesn't seem to have any useful effect. Bullet performance and shot placement are far more important, and adding power (velocity) often has negative effects on these two factors.
The .458 Win, .458 Lott, .450 Rigby and 460 Wby are all fine cartridges. In my opinion as power level goes up, so should gun weight. In a hunting rifle, a .458 win should be 9.5 lb, a .458 Lott 10.5, a 450 Rigby 11.5, and a 460 Wby 12.5 lb. Better to add weight to the gun than add a muzzle brake.