The short barrel is described in the game as:

Improves your mobility.

This can be found east of central Agua Verde in a cartel outpost. It’s a tiny open outpost on the bend of a road with about half-a-dozen cartel including a lieutenant. The accessory case it inside the armoury.

I kicked this approach off with a flare to distract the enemy, but a passing rebel pickup decided to get in on the action and we just killed everyone. There’s no awesome approach to this – it’s fairly simple to gun everyone down.

The short barrel essentially makes it easier for you to manoeuvre while aiming so you’re less sluggish, while sacrificing some range and accuracy and damage. Conversely the long barrel does the opposite, giving your gun more range and accuracy but making it more sluggish to move.

I’d say you probably want the manoeuvrability on an SMG and the range of the long barrel on a sniper rifle (found in San Mateo), so I wouldn’t recommend fitting this to a sniper rifle at all. However this is a very easy accessory to collect, so you’ll probably want to pick it up anyway.