I like it. I've never owned one, but reading the ballistics, it shows to be a true do anything caliber for North America, without the heavier recoil of the "above 30" crowd.
I think, IIRC, that it will give you 200-ish fps more per bullet weight than the '06... which is substantial. As a sort of cheap comparison, if the '06 is a 350yd deer rifle, the 300 would be a 450yd deer rifle. I think it would be much better for elk.
Any of the bigger calibers, however, come with a price... more expensive ammo, etc... Rifles generally are the same price range for the '06, 300, and 338 Win Mag... I think the rifles for the Lapua might be a little more pricey.
As I've gotten older, I've become more of a minimalist, caliber-wise. My "big" gun right now is a 1909 Argentine mauser that I turned into a .35 Whelen... which is simply an '06 necked up to 35 caliber. If I ever get to go for elk, I will simply have to limit my shots to under 300yds or so. Which is ok, because I've never had the desire to shoot an animal in the next county..
If I was going to buy a new rifle strictly for elk, I would very likely get either the 300 WinMag, or one of the newer "short" 300's. I MIGHT be tempted to go with a 375 Ruger, though.... I like the looks of that one, ballistically, although it might not have quite as flat a trajectory as the 300's...