I doubt any deer or bear is going to tell the difference when shot.
However, to try and at least contribute a little info here I'll say this.
1) The WSM will be a little faster with everything else being equal.
2) The SAUM case is .100 shorter than the WSM thus a little better suited to a short action, although I still run out of mag room with the 162 gr Amax, it's about .035 to long when seated .007 off the lands.
3) The SAUM has a longer neck than the WSM which some feel contributes to a more inherently accurate cartridge. Couldn't prove it by me, cuz I don't shoot "that" well.
4) The WSM does have the edge in brass, but with a little sorting Remington brass will get the job done.
I went with the Saum in a short action with a 27" barrel and it will run with the WSM in 24" barrel. If I were to do it again though I'd go with the WSM in a long action and never have to worry about OAL again.