If I had only one rifle
If I had only one rifle to hunt big game life would be both more simple and more difficult. Having different tools for different jobs makes sense but what would I choose if I was forced to change my ways.
If the choice was for one rifle to hunt the world I would choose a Winchester M 70 chambered in 375 H&H without hesitation. It would not be perfect for many things but it would do the job for everything.
If the choice was for one rifle to hunt North America it would be much more difficult for me. Probably it would be a Remington M 700 chambered in 30-06, but a 300 WM might be better. Of course a 338 WM would work well in this role also. I would lose sleep making this decision.