The purpose of both is to make small bubbles and swirl the water around. I have both an airstone and also an attachment that adds bubbles to my filter outlet. I actually find the airstone more useful for two reasons:
1) When doing powdered food like Bacter AE, I turn off the filter so as not to draw the particles into the sponge. I found that the airstone actually creates a lot of water swirling even on the far side of the tank.
2) For the same reason, if doing a H2O2 treatment where you don't want to drag water thru the filter media, the airstone is good
The advantage of the venturi-type system is that if you adjust it right, to have only a few bubbles worth of air intake per second, it can actually be nearly silent