The objective of hunting is to cause the destruction of vital organs; e.g. heart and/or lungs. What caliber & bullet accomplishes this objective is immaterial. As long as caliber & bullet penetrates vital organs, animals will die. Nothing will live long w/o functioning heart and/or lungs. That's merely simple biology.
God only knows how many North American big game animals have fallen to surplus .303 British rifles and Winchester 94's.
If I were to begin anew I'd buy a .280 Remington and never look back. But what I knew when I did buy big game rifles wasn't what I should have known. That hindsight bromide does come into play.
The two most accurate rifles I have fired were both chambered for 7MM Rem Mag, one a 700 ADL & the other a Sako. Both shot quarter-size groups.
The benefit of .284 caliber is sectional density. .284 bullets have mystical ability to penetrate.
Hunters should buy rifles that are right for them. Some hunters don't. Last year I watched a studly dude who was probably in his mid-30's sight in his brand new .300 Win Mag. He told me it was his first big game rifle. Up until that point he used relatives' rifles. His groups were about 6" at a hundred yards. He flinched with every round. He borrowed my shooting rest. He still flinched. After nearly a box of empty cases, he told me that he couldn't continue because of shoulder pain. In contrast, I had about a .75" group a couple inches high & dead center at a hundred yards. I was shooting a .308 Win. One shot, one buck. I hope that that dude did as well.
While I love the 7MM Rem Mag, it is not necessary to kill any big game animal. The 7x57 was performing that task quite admirably before the 7MM Rem Mag came along. Whatever a .300 Win Mag will do -with very few exceptions- so will an '06 or .308 Win. It's all about where a bullet winds up. A .243 Win in vitals is a lot better than an '06 in guts.
Did I mention that were I to start anew I'd buy a .280 Rem & never look back?
I hope this helps.