badsection and jimincolo hit the nail square on the head, bullet placement is more important than bullet diameter.
When I moved to Steamboat Springs in the late 60's I asked this same question to the locals that I worked with there. Their answer was either the .270 Win or the .30-06. They commented that only the city dudes from Denver brought up big guns like the .300 Win to hunt elk. I then killed my first elk, a 5x5 bull, with a borrowed .30-40 Krag, and I followed their advise and built my first centerfire rifle, a .30-06 that I then used to kill 8 of my first 10 elk.
When I moved to Montana in the mid 70's, my new hunting partner showed me a .30 Gibbs cartridge, and I thought that it looked so cool that I had my .30-06 rechambered to that cartridge. I then killed 20 some elk and a couple of Shiras moose bulls with that cartridge shooting 180 grain Nobler Partition bullets.
The ballistics of the .30 Gibbs is very close to the .300 Win which I now think is an outstanding elk cartridge, one because it is flat shooting and has sufficient energy for elk, and two because I think it is about the most powerful cartridge that most people can shoot without becoming afraid of the recoil of their rifle.
Several years ago I retired my .30 Gibbs and built my dream elk rifle, a .300 Weatherby. With this rifle I've killed bull elk with both Barnes TSX and TTSX 168 grain bullets, but I am now switching to 180 grain TTSX bullets.