As a specialization of the Minmatar, whose ships have the lowest capacitor, they require no capacitor and only ammunition.
This attribute makes them desirable on all capacitor intensive ships (not just Minmatar). If you fight against ships with many Neutralizers, it can be one of the only weapons that will still work.
Projectiles also have another attribute that makes them useful for PvE work: the ability to choose the type of damage by switching ammunition. It can also be useful, in PvP, against tankers that harden specific types a lot, yet leave other types open... although the target ship would have to harden their Thermal and Kinetic resistances a lot in order to close the gap sufficiently between Hybrids and Projectiles. Much of the time, you'd do better against BOTH shield tanks and armor tanks by using a Blaster, even though you can switch damage types.
Artillery Cannons are the weapons with the highest damage per volley, but the lowest damage per second, due to their low fire-rate. Because of this, they are superior instapop weapons where large fleets are concerned, provided range isn't an issue. They edge out Beam Lasers in effective range, able to reach out a bit further and do more damage at that range. This doesn't consider potential resistances, which will likely favor the Artillery even more. Railguns outrange the Artillery by a significant amount, while doing a lot more DPS given a longer period of time.
Autocannons have the lowest DPS amongst short range turrets, resistances notwithstanding. They can close the gap significantly by equipping an appropriate ammo type, although Blasters will still do better most of the time. Pulse Lasers will do better against Shields, but nowhere near as well against Armor. Autocannons also feature the highest tracking rate, highest firing rate, and 2nd highest effective range amongst short range turrets. These attributes make them best for dealing with fast moving targets with lower HP, such as Drones.
They may not be the best when it comes to range or damage, but they aren't the worst either. The simple fact that they require no capacitor makes them excellent alternatives to their brethren.