GL_ARB_point_sprite

1) You need 1/4 as many vertices. Point sprites just need one vertex per particle, while while quads need four per pixel.

2) Speed. When using quads, the calculations that ensure that the particle is facing the viewer are done on the CPU. With point sprites, they're done on the video card.

However, using quads gives you absolute control over how they're rendered.

But, the advent of shaders complicate things. You can do the calculations on the video card if you write an appropriate vertex shader.

So my advice is this: if you don't want to use a vertex shader, then use point sprites. If you do want to use shaders, then render quads, and offload the calculations to a vertex shader.