I use bias binding for anything that has a curve or shaped edge because the stretch of the bias will enable the binding to mould around the edges of the work. I do not use bias binding on straight edged quilts as it can 'rope' and ripple.
For straight edge quilts I use binding cut on the straight grain parallel to the selvedge, and not across the WOF. This grainline has the least stretch and gives the firmest, straightest edge to a quilt. Binding cut straight across the WOF is stretchier than binding cut parallel to the selvedge. Try stretching the two straight grains of a piece of quilting fabric to see what I mean about the differences in straight grain stretch!