HUGE!!!
My step-dad has shot the 'o6 for years and has killed everything up to and including elk. Now that I live in Alaska I have spoken with a few "old timers" and they tell similar stories. There aren't many animals on this grand old continent that have stood up to the 30-06.
That being said, my wife just happened to buy me a Sako 75 Hunter in 300 RUM for my graduation present!!! (I love that woman!!!) I wouldn't trade it for anything. Plus, coyotes don't stand much of a chance with a 110 grain bullet doing over 4000 fps
!!!
If you want to look at it in energy, the 300 RUM can produce over 4500 foot-pounds at the muzzle while the 30-06 max power stays around the 3000 foot-pound range. Don't let this fool you, though. The very popular 300 Win Mag sticks around the 3500 foot-pound range and is very well regarded in any hunting/shooting circle.
As far as I know, the 300 RUM is the most powerful 30 cal out there except for the 30-378 Weatherby. That may not be 100% accurate, but it is based off of all the load data, reloading manuals and charts that I can find.
If you like to shoot a lot then the 300 RUM might not be for you. The '06 is cheaper to shoot, reload, buy ammo for and more pleasant on the body. I forgot my sissy pad the other day
and only took 7 shots before I put it away! I does shoot flat and fast, though.
Hope this helps a little. Hopefully more chime in with some opinions.