I'm thinking that you have an asymetrical bevel but that is not the cause of the uneven sharpness. The asymetrical bevel is causing the sharpmaker to hit the edge on one side only and that it's causing a burr that can't be removed by stroking on the other side because the other side of the bevel is not hitting the edge. You are basically hitting the shoulder on the bevel on the side of the knife that seems sharper to you.
A quick fix is using the sharpie trick. Color the bevels with a sharpie and go back to the sharpmaker. After a couple dozen strokes, look at the bevels again, preferably with magnification. You'll be able to see what part of the bevel on each side the stone is hitting.
After you see which side of the bevel is not being hit to the edge, then while you stroke the side(whose bevel is not being hit all the way to the edge) of the knife, tilt the spine away from the stone in sufficient angle that the stone will hit the edge of the bevel.
One more thing, burrs often need an educated finger to feel. A good way to test for a burr is to wipe a cotton ball on the bevel in a spine to edge direction. If it catches, then there's a burr.
It is nevertheless not the asymetrical bevel that is causing the unequal performance between sides but it is the asymetrical bevel combined with the fixed angles of the sharpmaker that is causing the burr that is causing the erratic performance.