Although the .300 WM will buy you a longer effective range (maybe 75 to 100 yards) I think it's biggest advantage comes by using heavier bullets. I never shoot bullets weighing less than 180 grains from my .300 WM and have had good results with 200 grain pills. When I use a .30-06 the heaviest bullet I shoot is a 180 but more often I use 150 or 165 grain bullets.

Both cartridges have advantages over the other but at the end of the day they are both .308" and for most practical hunting ranges both cartridges will do the job just fine.