What exactly do you get from different slings in Angry Birds Friends?

Wishbone increases damage just like the gold one. Bubble one increases bounciness of birds: for example, it's useful when you want to hit structures from below by bouncing the bird from the ground. The diamond one shoots the bird in a straight line (gravity doesn't drag them down). The xmas tree with ornament shower is also very useful because of the extra damage from the ornaments.

I hope this helps!