Almost nothing. You can test this yourself if you have the skills to make a mouthpiece ultra symmetric. Any one area you then make non-symmentric will not be noticeable on a play test. After you make a bunch of changes, they may add up to being significant. But this will most likely be due to the fact that you made the chamber volume a little larger with all your changes.
Now the facing curve on the side rails is another story. The window can be off-center so the the side rail thickness is not the same. This mostly a cosmetic thing. But the piece will play its best if the facing curve is a good shape and symmetric on both side rails.
Natural selection dictates that we prefer symmetry. It is a perceived sign of quality even if it does not effect the function.
Now the facing curve on the side rails is another story. The window can be off-center so the the side rail thickness is not the same. This mostly a cosmetic thing. But the piece will play its best if the facing curve is a good shape and symmetric on both side rails.
Natural selection dictates that we prefer symmetry. It is a perceived sign of quality even if it does not effect the function.
