The Long Barrel increases the range of a weapon by 16%. Therefore, the longer the initial range of a gun is, the longer the maximum range will be. The attachment is available for submachine guns, shotguns and handguns. It is incompatible with the suppressor attachment, for balancing reasons.
The Long Barrel appears as an attachment for several weapons in Call of Duty: Black Ops III. It increases the effective range of a weapon. Aesthetically, it adds an extension to a weapon's muzzle. It is now compatible with the Suppressor barrel attachment.
Call of Duty: Black Ops II
The only weapons to actually change appearance cosmetically when outfitted with the Long Barrel are the Executioner and the Olympia.
The Long Barrel doesn't actually increase the damage inflicted. Despite the statistic increase, rather it increases the distance of the damage drop-off by increasing the range.