On the other hand, there's a few moves which if I wait for them to be as good on the bad side as they are on the good side, I'll be waiting a *long* time. In yesterday's class sensei looked at my koho tento undo (left foot forward) and said, "Wow, you've been working on that, it really shows!" Unfortunately then we did the right foot forward; he winced and said "Well, one side is always harder than the other." I figure I'll only annoy myself if I compare the two, so I'm just working on making both of them better.
Bokken work, and unarmed-versus-bokken, might be the exception to the symmetry rule. I've been taught some bokken takeaways that do not work the same on the other side, and one that doesn't work at all (unless you meet a left-handed swordsman, and I'm told that doesn't really happen in the Japanese sword arts).
I think learning something on both sides makes you know it a little better--I have poor ability to "visualize" kinesthetically, and I find that trying to mirror-reverse what I've just been taught helps me develop that ability.