As far as I know, it has the same effect as Steady Aim Pro did in MW3, where it decreases the delay between running and shooting. I know the perk description only mentions faster ADS after sprinting, but I did some tests and it seems as though shooting in general is just much quicker after sprinting.
Not sure if people knew this already, but try it out on shotguns and see if it helps :)
Unless you like climbing fast, Dexterity is really only useful on LMGs, and that's only if you're going to be running and gunning with one, which isn't a frequent playstyle among LMG users. This video analyzes the perk, and shows it's uselessness.