I always measure through the middle first, then cut the borders to size. I quarter both quilt edge and border and pin to match up the ends and those marks. (If it's a really large quilt, I will do eighths.) I stretch or ease the border as necessary to match everything up.
Sewing the border on first and the cutting off the excess almost guarantees sewing excess border to the quilt edge. This in turn makes the quilt edge finish with rippling along the edge or wavy borders.