Faster where ? on the CPU ? The amount of work for a full screen quad is negligeable on the CPU compared to the work required to happen on the GPU.
So what matters most in this case is usually to optimize the GPU side, and believe it or not, there is one thing that is fairly significant. All the GPUs I know internally convert a quad to 2 triangles. Each of those triangles get rasterized separately. As it happens, you end up not using the GPU to its fullest, because on the diagonal between the 2 triangles, the GPU will have to work twice (this is because the GPU works on typically 16 or 32 pixels at once, in shapes of square or rectangle. The minimum is 4, which is already doing extra work).
How to avoid that extra work on the edge ? Draw a single triangle over the full region, and scissor to the region you want to draw to.
Something like (although I usually go from 0 to 1 rather than -1 to 1...):
glBegin(GL_TRIANGLES);
glVertex(-1,-1,0); glVertex(3,-1,0); Vertex(-1,3,0);
glEnd();