I've had all 3. I've never noted enough difference in accuracy to matter. I hunted with a 30-06 starting in the 1970's up until about 10 years ago when I started using 308. I've experimented with both the 300 WM and 300 WSM, but simply don't need the power.
Why do I now prefer 308 over 30-06? My 308 gives me 95-97% of the bullet speed of a 30-06 with the same bullets and 20-25% less recoil. That loss of bullet speed means my 308 does exactly the same thing at 450 yards that the 30-06 does at 500 and a 300 WM does at 600. I can't shoot well enough to be shooting at game much past 300 yards. Maybe 400 under ideal conditions.