Some thoughts come to mind, the supplied jig is not necessarily of the best design and, if used with too coarse a wheel, might not sharpen both cutting edges equally. The supplied jig is a compromise design for both turning and threading and because of this it tends to put striations along the length of one of the cutting edges which will not be as sharp as the other. A 30 degree vee shaped jig held at right angles to the wheel is, in my view, to be preferred as it puts an equal grind on both edges.
Another thought is have you put enough of a radius down the length of the tool bit. A sharp corner does not seem to cut as well as a radius one. If you put different radii on opposite corners and sharpen both ends you can select the either end for different needs.
A tangential tool will often give a superior cut on the back stroke, due to a sheering action, but should still cut forwards almost as well if ground well..