Plug in the numbers yourself
http://www.handloads.com/calc/recoil.asp
These are actual loads that I've used or are still using. Not top end, I can get another 100 fps out of either, but the ones that proved to be the best combo of speed and accuracy. It is possible to play around with various load combos and make the end result come out any way you want it to. I tried not to do that by selecting loads that I've actually used and have worked for me.
300 WM 180 gr @ 3000 fps with 75 gr powder in an 8 lb rifle
27.95 ft lbs recoil
300 WSM 180 gr @ 2950 fps with 64 gr powder in an 8 lb rifle
24.53 ft lbs recoil
OK, so it's about 14% less recoil and about 14% less powder and 1.7% less speed. Pretty close for estimating off the top of my head.
For reference my 8 lb 30-06 shooting 180's @ 2800 fps would generate about 22 ft lbs of recoil.
The 300 WSM is pretty efficient as to powder and recoil. It comes close enough to 300 WM to not matter with recoil about 1/2 way between 30-06 and 300 WM.
This is exactly what Jamison was attempting to achieve when he developed the round. The real purpose was to be able to package it in a lighter, trimmer rifle without excessive recoil. In the real world most 300 WM's would be about 9 lbs instead of 8 lbs. At that weight difference you wouldn't notice any difference. My 300 WSM weighs 6.5 lbs, about 7.5 lbs ready to hunt. I wouldn't want to shoot a 300 WM in a rifle that light.