If you load your own bullets you can simply press light loads.
I don't personally own a WM but I do own a 300WSM which is pretty similar. Just cause the case is there doesn't mean it has to be packed full of powder with the biggest .308 caliber bullet you can find rammed in the top.
I have a load that is rather nice to shoot that sends a 165gr cheapo Sierra spbt downrange at2600fps and group into 1/2" at 100yards .
But for the full potential I have a load sending a 200gr Accubond 3000fps grouping 5/8" that is a gun I can take anything from Predators to Deer to Bear.
A 300WM if hand loaded could probably do as good or better than that.
Not hating on the 06 or anything but performance speaks for itself.