Although I love the .30-06 and the .308, I believe they are not the ultimate one caliber for North America, or anywhere else. Ya, if you don't reload, and rarely hunt anything big, they are probably a great choice.
For those who hunt everything, on this continent or the Dark one,
338 WINCHESTER MAG is the only way to go.
As flat as a .300 with the same weight bullets, but can handle the .250gr bullets with style and speed. Load it down with 180gr for varmints(heheheh) or load it heavy for elk, lion, moose, bear, .....you name it.
My load for hunting antelope to elk is 250grSGK in front of 71gr. of IMR4831. Out of a 24" barrel, I am getting an average of 2800fps. It is a max load, and also compressed, so load it down first to see how it handles in your rifle.
It doesn't kick anymore than a .300win, but has more punch for you game. You can load it to duplicate the .300win; just as flat, just as fast, or you can make it a thumper, almost as fast, almost as flat, but with a lot more knock down power.
I also like the .270win, if you intend most of your game to be smaller than moose. Maybe, focusing on the varmints(coyotes, fox, ect.), this would be the caliber for you.
You did ask what was the best all around HUNTING cartridge. .338Winmag is the answer to that question, period.