This question sounds like a riddle.
In theory, the edge is an apex--a point--an edge can't have "sides", so there can't be a sharp side or a dull side.
I suppose one edge bevel could be more refined than the other. I forget who, but there was (at least) one sharpener who finished each edge bevel at different grits. I also forget what the logic was.
If there are burrs still hanging on, I'm going to guess and say that, if it shaces, the "up" side not the "arm" side has the burr. I think the burr would interfere more with cutting if dragging against the arm ("down") than dragging against nothing ("up"). But this is just a guess, and there are many other variable that could enter in. For example, what if it's a foil edge and flip-flops, so the shaving is really more like stropping?... Then, the side won't matter, what will matter is first-vs-second stroke, since the first stroke would flip (or drag) the burr. So, the second stroke would either be worse (or better) than the first irrespective of the side.
Again--just spitballin here... so put this in the "best guess" bin.