I read an article several years ago recommending the 338 mag for North America.
IMHO the 30-06 isn't big enough for grizzly/brown bear.
My father has used a 338 mag Ruger M77 for 20 years or so. He reloads his own ammo for different game. He has taken every big game animal in Alaska except musk ox and polar bear.
When I was 14 or 15 I went on my first bear hunt. Since it was my first, I got to shoot first.
We scoped a brownie about 250 yards away. We couldn't get closer to him so we waited for him to come to us. Which he did until my uncle sneezed.
The bear turned and walk away but then stopped, turned around and came towards us very slowly. My dad said shoot so I did. First round through the front of the chest. Second round through the right shoulder.
We made a mistake in letting the bear know where we were because he immediately charged toward us. I fired again but missed.
My dad then shot him once through the high chest area. The bullet went through the spine and exited dropping the bear immediately. The bear was only 200 feet away.
I was shooting a Weatherby 30-06. My dad a 338 mag. My uncle had climbed the nearest tree with his 30-30.
A week later I had my own 338.
I realize that shot placement is everything, but for large game I would rather have a bigger caliber.
It all depends on how and what you hunt.
Don't become the hunted.

