Generally, I don't consider the ~300fps differential between the 30-06 and 300wm, but rather, I consider the 300wm is capable of considerably heavier bullets without sacrificing significant velocity impacts. I can get 220's to the same speed in the WM as I can the 178's in the 06. I don't generally go all the way to the 220's, but shooting the 208's and 212's gives me about 0.15 boost in BC (recoil be d@mned).
That extra weight might not mean much for a guy, and certainly doesn't mean anything until a guy is talking "heavier than elk" game, otherwise you're just punching a bigger hole in the dirt on the back side.
The 30-06 will do anything a guy asks it to do on the American continents, and until you get to dangerous game in Africa, which generally require 375 & larger anyway, the .30-06 will keep you well armed on any "whitetail and up" game.
The only downside, I might mention, despite being a Ruger fan myself - the Hawkeye's are heavy, and since you mentioned "mountain rifle," that's a consideration. The extra weight is certainly nice to tame recoil in the 30-06, but for hauling that thing up and down and 'round and 'round, they end up about a pound and a half heavier than you might find in a Remington 700. I've never struggled to carry heavy rifles in the field, but some guys become real weight weenies when you start talking "mountain rifles."