The method most quilters use is single-fold straight grain binding. It's not cut on the bias. Basically you make a long strip about 2.5" wide and fold it so it is only half as wide. This gives the binding two layers of fabric. The binding on a quilt is the area that takes the most abuse, so having a double-layer of binding on the edge helps the quilt last longer.
For me, there are no disadvantages to using this binding method instead of folding over from the back. I suppose it takes a little longer.