Hi,
If a fabric is a directional print or design I do not piece it, but cut it from the length of fabric. If I piece a border I piece them diagonally and you usually don't even see it, especially once it is quilted. I piece borders more than do them one piece.
I will sometimes do a scrappy border with pieces left from the blocks. I also sometimes use a scrappy binding. It can add a bit of color and zip to a quilt, depends on the pattern and fabrics in the quilt.
bev