No I don't think they are identical, I just don't see the runner having an advantage, which is the only place its really relevant. I do know that the left catcher has a huge advantage over the RH catcher on bunt plays. But you don't see anyone discouraging RH kids from catching over it.
Runner has the advantage because all other things being equal, it will take the catcher longer to release the ball (by a small fraction of a second) being lefty.... That could be the difference between safe and out.