A lot depends on the planning. Cutting fabric for a border the length of the fabric requires you to know how large the quilt will be AND you need to cut the border strips BEFORE everything else to ensure that you have enough.
I usually piece my border strips and cut across the fabric which means I end up with strips the width of the fabric.
Cutting on the bias means that you cut across the fabric at a 45-degree angle. I don't think that is a preferred way to do it because bias cuts are easily distorted - they are the stretchiest.