Not sure I agree with what you are saying. Both rounds are short action magnum rounds. Both have the same parent case, the 404 jefferies
Both were designed to deliver near magnum performance in a short action, hence the names, winchester SHORT magnum and Remington SHORT action Ultra magnum
Both a normally chambered in short actions, though many folks chamber them in long actions in order to seat the bullets out farther. Putting either one in the short action will hamper them equally.
The case length for the WSM is 2.1 inches, for the SAUM 2.015.
The WSM has a bit more case capacity, The SAUM has a very slightly longer neck and is actually a bit more efficient.
There are actually rifles chambered in WSM, even Remington chambers the 700, I don't think they chamber a rifle in SAUM.
There isn't enough difference between the two to worry about, check sources for brass and let that be the deciding factor