I've owned several 300 WM rifles, several 30-06's and one 300 WSM. My WSM was a Winchester SS Classic that I had in a McMillan Edge stock. With a Leupold VX-2 3-9X40 scope on it in Talley LIghtweight mounts it weighed exactly 7 1/2 lbs. The same as a my 30-06 set up in a similar way. Recoil was only slightly more than my 30-06 of the same weight, but a lightweight 30-06 can be sporty.
A 300 WSM comes within 50-75 fps of what you can do with a 300 WM, and will beat 30-06 by about 200 fps with 180's. But since it uses quite a bit less powder than 300 WM recoil in same weight rifles is noticeably less. Doing the math with my loads through a recoil calculator my 30-06/180@ 2800 fps hit me with about 22 ft lbs recoil. My 300WSM/180@ 3050 hit me with about 28 ft lbs recoil and a 300 WM/180@ 3100 fps was 33 ft lbs recoil. 300 WSM is right down the middle in recoil, 6 ft lbs more than 30-06, but 5 less than 300 WM. To me, I scarcely noticed the 6 ft lb difference between 30-06 and 300 WSM. I did notice the 11 ft lbs between 30-06 and 300 WM.
I found was that a 300 WSM in a 7 1/2 lb rifle recoiled exactly the same as a 300 WM in an 8 1/2 lb rifle or a 30-06 from a 7 lb rifle. I like the 300 WSM. If I'm looking at the same recoil as 300 WM anyway, but can carry a 1 lb lighter rifle while only giving up 50 fps I'd make that trade every time.