The short barrel is described as:
Improves your mobility.
You’ll find this south of central Agua Verde in the huge Agua Verde Base, a Santa Blanca base on a peninsula. The accessory case is inside the armoury near the helipad. This base is obviously crawling with enemies.
This is definitely easiest to approach at night time, and the simplest way in is via the small islands from the north-west, simply because the land approach is blocked by a gate, and the armoury is a lot nearer the tip of the peninsula than the gate. At night, there will be fewer enemies in your path and you can just take out some lights and the ones that are in your way.
The short barrel essentially makes it easier for you to manoeuvre while aiming so you’re less sluggish, while sacrificing some range and accuracy. 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 on a sniper rifle, but with an AR it depends a lot on your play style. If you run and gun with an AR, then you may want to give the short barrel a try. If you keep your distance then this might not be for you.