OK, I am anal -- if I am doing a border that covers a long length (over 12"), and it is directional, I do one of the following:
-- cut it so the pattern is going up and down -- the tops are cross cut and the sides are cut vertically
-- cross cut both top and sides and face them to the center
-- cross cut both top and sides and face them out
My decision is based on the width of the border and how it looks cross cut versus horizontal -- and how much fabric I have. I find that linear patterns are harder to cut vertically for the sides (there is a whole issue about patterns not being printed truly on the grain).