I will have to agree with everything said so far, except for the comment about the recoil.
The short fat powder column is supposed to burn more uniformly. As a result, you get more velocity per grain of powder, and better accuracy.
The short mags fit in a short action, which is shorter and stiffer than a long action, thereby more accurate.
The shortmags also headspace off of the shoulder instead of a belt.
Regarding the question of recoil: I have shot 300 Winmags and of course, my 300WSM in a Winchester Model 70 featherweight (7 1-4 lbs).
It seemed like the short mag kicked a LOT less than the winmag (shooting similar weight bullets and powder charges).
Last year I started loading 165 grain Nosler Partitions for my 300WSM and I've gotta tell ya'.....it is one sweet shooting load. I can shoot it from the bench pretty much all day without a puss pad, and not have a sore shoulder the next day. By the way, this load is one heck of an elk killer. It's killed three (two full grown cows and one calf) this year.
Don't get me wrong, if you shoot max 180 grain loads, they'll kick you, especially from the bench. I just don't think they kick as hard from a 300WSM as from a 300Win mag.