This business of balancing on the pin etc means little. You can balance a gun on the cross pin while hanging ten kilo weights on either end.

I suspect that what most people mean by balance is handling. The main thing there is to have a gun that does not fight you when you move it, ie has most of its mass in the part between the hands. This is not exclusively a best gun feature. In a blind test described in a British magazine a humble Bernardelli Ellio 16g came out as best handling.