The 300 WSM may offer an advantage which I personally won't be able to discern over a .30-06, and if it does, it will be at ranges that I personally do not shoot.
My $.02:
If you need to go bigger than a '06, go BIGGER: .338WM, .35 Whelen, .375 H&H.
If you need to go faster/flatter than a '06, go FASTER: .300 RUM, .30-338 WBY, etc.
FC