Around here they do both or either depending on what you want, except for The Quilt Patch, she says she would turn away a customer that wanted fabric cut. I thought that was a little extreme, but it's her shop. When I was discussing this with one shop owner who preferred to cut she said the tearing sound makes her think the fabric is screaming, little creepy, huh.
Now for me, I always tear my borders along the length of the fabric, not the width of the fabric.