I think casdave and Mersavets might be talking across each other a little bit about the physics of braking. Not that this is directly related to handle side convention.
Anyway, here’s the physics of the situation:
Braking EITHER the front or the rear wheel is going to cause the whole bike to rotate about the center of mass of the bike (& rider). The rotation will tend to lift up the rear wheel and push down the front wheel. However, the front wheel can’t really move down very far (the ground gets in the way), so the center of mass starts rotating about (and eventually up and over) the front wheel, with disastrous consequences to the rider if taken too far.
The rotation is the same no matter which wheel is braked (broked? braken?). But as weight comes off of the back wheel, it has less braking power – if you brake hard enough to lift the back wheel, it has NO braking power anymore. So it’s just about impossible to flip the bike over forwards using the rear brake.
So the rear brake is safer but has less braking power. In theory, the ideal method to stop most quickly is to put on the front brake just to the point where the rear wheel begins to lift, then hold it there. There’s some debate in the bicycling community about how close a human under actual road conditions can come to the ideal and therefore what the best quick-stop braking strategies are. (For automobiles, the center of mass is low enough that they’ll skid before flipping forward, so this is irrelevant. I have no idea about motorcycles).