I usually stitch them straight across. Actually, I will stitch binding on the diagonal but not borders. It never occurred to me to do the borders as a diagonal. I may have to try that.
I do use a lot of prints, so the seam isn't as visible as if you are using a solid fabric. Before quilting and washing, the seams can be very visible. After the quilting process and washing, most times, I can't even see where I seamed the border, even if it is a solid.