While I do not own a .300 Win Mag, I have a lot of respect for it. It is a formidable cartridge, capable of killing everything on our continent. However, many cartridges have killed everything on our continent long before someone decided to put belts on cartridges.
Within reason, a cartridge ain't as important as interrupting a big game animal's ability to pump oxygenated blood to its brain. Biology is controlling. Put a bullet from any suitable big game cartridge into an animal's heart and/or lungs and it will die.
Were I given a hunting do-over, I'd buy a good-quality .280 Rem and never look back. But others assuredly feel the same way about many other cartridges.
I do admire men who can shoot big bore rifles, especially off benches. I'll be right up front with my limiting my recoil threshold to the 7MM Rem Mag. I have an original Guide Gun. I've fired about three hand loaded .45/70 Gov't rounds filled with a healthy dose of IMR-3031 & a 400 grain Speer bullet. That gun about knocked me back to the Middle Ages. I doubt whether Muhammad Ali hit harder. I have fired other big rifles including the mighty .300 Win Mag. I'm good with a 7MM Rem Mag.
The .300 Win Mag is popular because it works as advertised. Whether it will kill any better than an '06 is doubtful.
An adage I learned too many years ago to remember when I first heard it goes like this: a .243 Win to the boiler room is a whole lot better than an '06 in the guts. It was true then, and it still is.