The right - where everyone should wear their computer.
I say it with a smile, but I am actually serious. Your left hand is for controlling your buoyancy compensation. You should be able to look at your computer and monitor your depth while you are adding or dumping as from your BCD. It's even more important in a rescue scenario, where you might be attempting to surface with a non-responsive diver. In that case, your left hand will be controlling buoyancy compensation - possibly yours or possibly theirs. And your right hand may be reaching around from behind to hold their reg in their mouth. In that scenario, it really needs to be on your right wrist if you're going to have any chance of monitoring your depth as you ascend.
What if you are on a recreational dive on a wreck and, for safety reasons, you really need to get back to the anchor line before you start your ascent? And if you are relying on your compass to help you find your way back to said anchor line?
As with any other gear in diving, if you NEED it during the dive, then you should give some solid thought to whether to carry redundancy on whatever it is. If your backup is the one your buddy is carrying, then fine. But, make that decision consciously. And in this case, make sure your buddy also takes appropriate compass headings and doesn't just rely on you to get you back to the anchor line safely.