The comparison is based on the coating of barbells:
The black oxidation is also called as bluening, which is a passivation reaction. A dense oxide film on the surface of iron, which is isolated from iron and acts as a rust preventive.
Black zinc is a method of electroplating on the surface of barbell to produce a zinc layer. The activity of zinc is higher than iron, acid in the air reacts with zinc first to protect iron. After zinc plating, it passes through chromate. It produces a black passivation layer to enhance the protection of electro-galvanizing.
Besides, black zinc film is thicker than black oxide painting on Olympic bars.