The choice of cartridge is only one element to consider. The rifle needs to be appropriate to the conditions expected as well as appropriate to the game being hunted. I'm a .375 fan, but I'm also a .30/06 fan because both are so good. From the view point of hunting as opposed to bear work; I don't feel under-gunned with the '06 and I don't feel over-gunned with the .375. If I do my part, both rounds kill game, but if I screw up, both rounds will wound game.
I own rifles chambered in both cartridges that shoot better than I can hold, but I can shoot both rounds competently. The short, fast handling, .375 carbine with the scout scope is a better choice to solve close range problems than is the long barreled '06 with the fixed 6X scope. Conversely, in the open the 6X scope sometimes makes hitting a little easier, even though the the trajectory of both rifles is quite similar. While I could put a conventional scope on the .375, I'm just not comfortable with a scope that close to my face on an enthusiastic kicker. If I was hunting game that tends to blend in with it's background, particularly in open country, the 6X scope has the advantage and under such conditions the longer .30/06 posses little inconvenience.
Lastly, my .30/06 is my fair weather gun while my .375 can stand up to anything nature has to offer. Heat or cold, wet or dry, it never misses a beat. That's and my ability to hit with it out to 300 yards is primarily why it's my go to rifle. The fact that is has more power is of less concern in a Canadian or North American hunting scenario. The .30/06 when loaded with an appropriate bullet has a reasonable expectation of killing any North American big game with a single shot from any angle within the limitations of it's range. The same can be said of the the .375 and may other cartridges, but once we reduce bore size below 6.5 that is no longer true. The 6.5's are what I consider the lower end of what should be considered a general North American hunting cartridge. Small bore shooters, the 6mm's and quarter bores, must qualify the cartridge with specific shot placement, on specific species of game, but not so the 6.5's. This is not because of the difference between the frontal area of the .264" bullet and the .257" bullet, but because no one as yet produces a 150 gr .243" or .257" big game bullet.