Damage Output: A single slingshot bullet does not do very much damage. However, the slingshot has a very high rate of fire. If you have good accuracy, you will be able to hit your opponent multiple times, doing a lot of damage.
Accuracy: Unlike the superball, the slingshot automatically calculates the angle to use to hit the location under the targeting cursor. So if your enemy is behind a wall and only his head is showing, it is not hard to get him with the slingshot. Here's a fun thing to do: in Chaos Canyon get to the top of the big battle cube and shoot people below with a stream of slingshot bullets - it's easier than trying to nail them with rockets, since rockets move so slowly and can be dodged.
Defense: If you rush at someone head-on with the rocket launcher, and that person is using the slingshot, the person using the slingshot has a higher chance of winning. This is because your rocket will often hit one of the sling bullets and detonate before getting anywhere the person with the slingshot. All the while, you will be taking damage from the slingshot bullets. This defense works against superballs too (though it is less effective). Many people only use the rocket launcher, only to lose against more experienced players who use the slingshot. One way to defend yourself against someone who is up in your face with a slingshot is to use the slingshot against him, fire faster, and fire more accurately.