If yo look at the ballistics of the two calibers the 300 WSM
is the 308's big brother on steriods. It will out preform the 308 in every way.
I own the 300 wsm in a tikka t3 and shoot the 200 gr accubonds out if it at 3000 FPS with reloader 17. (They are HOT loads with slight craters in the primers.) It shoots well under MOA. I have taken elk at 814 yds.
So my two cents, go with the 300
But if I could do it again I would buy the 300 win. Brass is cheeper and more readily available.