Maybe as much as 3/4 inch. And the possible lenght of cartridges they can handle. That's about all, practically speaking.
Some folks claim to love short actions because they are two-three ounces lighter. It makes less than a quarter pound difference in most scoped, loaded rifles, all told. Not much. No difference in fatigue at the end of the day from carrying "a big, heavy long action."
Some folks think a short bolt throw is "faster" to operate. The bolt travel has about a 1/2" difference. Proper operation of that bolt, taking that last .5" of travel really doesn't take a lot of time, at least not for me. I can't figger what they are doing to take them so much time to work a bolt. ??
Mechanically, a shortened action IS a tiny bit stiffer than a longer one and more accurate because of it, in theory. Considering the small actual length change and normal accuracy limits of any factory sporter, I think they would have a hard time proving that theoritical premise on the range, never mind in the field.
So, the biggest difference is hype.
