I have opinions but since I've shot neither, take them for what they're worth.
First of all, I'm not a huge enthusiast of .270 caliber cartridges. If I were looking for a big game rifle, I'd go fore something bigger like a 7mm and for small game I would choose something smaller. In my opinion, for the game it's meant for, a 270 Winchester would work as well as the 270 WSM and 270WM. I'm aware that this is just personal bias. Jack O'Connor not withstanding, I could do without .270 caliber firearms of any description.
As for the 270 WSM vs 270 WM question; I see no reason for the 270 WSM in the first place but brass for it might be cheaper than brass for the 270 WM. Guns for the 270 WSM are also probably also cheaper than the Weatherbys. On the other hand, the 270 WM has been around for a lot longer than the 270 WSM so at least if has some enduring power and it would be my choice between the two.