I machine bind because it hurts my hands too much to hand stitch more than a few stitches. Therefore, none of my quilts would ever get finished if I hand quilted.
Advantages to hand stitching - if done right, you can hardly tell that it was stitched at all, very crisp, neat, finished, professional look.
Advantages to machine stitching - it's done, and it's done sooner. Less stress on my shoulders, arms, hands. I make a lot of charity quilts, so machine stitching gets them done sooner. I've heard people say that it makes the binding sturdier, but can't say one way or another if that's true. If you can use a decorative stitch on the binding, it gives a nice look, too.