The long barrel is described as:

Increases muzzle velocity

You can pick this up in northern Libertad province, at a Unidad observation post. The accessory case is on a crate behind a tent, off the road.

There are five soldiers in the vicinity. One near the case, three by the road and another wandering around a bit further down. It’s very easy to stealth kill them with a sync shot. Then just run up and you’re done.

The long barrel for shotguns increases damage and range a little, and reduces handling a little. For the SASG-12 (found in Agua Verde) it also increases accuracy slightly as well, but has a more pronounced effect on handling. So, depending on which shotgun you use, you may choose to equip this or not.

If you want the extra range and damage, then it might be worthwhile. But if you rock the SASG-12 then I don’t recommend this, because being fast firing you probably want to spray down your foes and that loss of handling could be detrimental.