I think this debate depends quite a bit on where your base line assumptions have been formed and in what culture your hunting habits were developed in.
I grew up in Canada. Western Canada to be precise. I was born in the middle of the last century, when The most common, widely used, good for "anything" cartridge was the .303 British. It was the normal baseline of adequate performance for the average hunter in Saskatchewan who pursued whitetail deer and mule deer, elk, black bear and moose. Nobody in their right mind with any experience would say the .303 was inadequate or a poor choice for those game animals. I laugh when reading of people who think they "need" something bigger for moose. Millions of practical examples in the field attested to the effectiveness of the .303. All my hunting mentors started out with .303 "sporter" rifles, actually just cut down military Lee Enfield SMLE's. I shot my first game animal with one too.
About the time I started hunting, the "new" .308 Winchester replaced the .303 with the following benefits. Better accuracy, slightly improved power, the same 150-180 gr. bullet weights in common hunting use, while chambered in more modern, handier and overall better and more accurate rifles. And cheap military ammo was widely available for practise and varmint blasting.
There was nothing not to like, and everything to like about the .308.
I suspect that same fondness for the .308 in Canada translates at least in part to many hunters in Great Britain and Australia and New Zealand and South Africa.
Nearly the same sequence of events could be said about the USA, substituting the .30-40 Krag for the .303. Same-Same performance in the field. But the Krag dropped away much earlier, and then the USA replaced the Krag with the .30-06.
I like the .30-06 a lot, and have a couple .30-06 rifles that I enjoy hunting with. But "better" than the .308 is certainly debatable. I don't buy into the argument that bigger is always better. Sometimes, a cartridge is, as Goldilocks said while tasting porridge - "just right". I think the .308 is it. It's a Goldilocks cartridge.
Canada has a population only 10% of the USA, and with a much smaller manufacturing base and market share of North American firearms. So the USA has dominated the choices of Canadian hunters to a large extent. And international hunters too. As a result, many Canadians would choose the .30-06 as their favourite. I'm not sure that's based on merit, just markets and habit.
If I feel a need for more certain results while hunting very large animals at normal shot distances under 300 M, I choose something bigger than .30 caliber. That's what my .35 Whelen, 9.3x62, and .375 H&H rifles are for. I personally have no desire to turn hunting into a sniping competition, so .30 caliber magnums with their long range capabilities are of no particular interest to me.
There is nothing wrong with the .30-06. But I'd argue that for hunting mid-size animals appropriate for .30 calibers at reasonable ranges, the .308 is "Just right" and the .30-06 is "just as good" - but not better.
there may be better choices, but the’06 is never a bad choice.
