I have not and probably never will hunt elk. I have however hunted both deer and moose. There are too many unknown variables to make a call on this one.
There are many rifles capable of taking all three animals but the things that will narrow that group down to "what is best" is which one is best suited for the environment you will be hunting (short range or long for example) and more importantly which rifle you are the most comfortable and accurate with.
For me the best is my 45-70. For you it may be the 30-06. I know some people that swear by the 30-30 for moose and although I would never use it they have backed up their claims by tagging out just as cuccessful as the guys out using 300 Weatherby Mags.
Make your own decision based on the capabilities and/or limitations of the environment, the firearm, and most importantly yourself.