Having shot and had semi customs built on both, the only difference I can see is that not all stocks are available for both. As an example, you might find a given company has only a hunting stock for long action, but offers both a precision and hunting stock for the short action. Before you commit to one or the other, make sure the accessories you want are available.
I dont buy the "stiffer and more accurate" and "quicker to cycle" arguments. If there is any truth to them, the differences would be so small that the many other facets that factors into it (such as accuracy of the barrel, ease of manipulating the trigger accurately, shooter's talents, etc) would dwarf and negate any advantage you gain by going short action. Joed nailed it, his explanation is sound, IMO.