Does it matter what direction a herringbone gear turns?

Obviously, the forces and pressures should mostly be the same, but just in reverse. But when play, flex, and such are accounted for, are there any subtle differences to having a herringbone gear turn in different directions?

Intuitively, I might suspect that it would be preferable to turn towards the centerline, so that the first point of contact on each tooth isn’t near either edge.