The major differences between these three coloring materials will be in terms of production techniques and color rendering.
Synthetic Enamel is probably the best material to render bright and shiny for colors in a reasonable cost. Colors are leveled evenly to the metal boarders and totally flat on the product surface.
Hard Enamel differ from Soft and Synthetic Enamel. It is natural mineral substance and melted during heating process. It is not as bright and shiny as Soft and Synthetic Enamel, but the color lasts for hundred of years without destroying on purpose.
Soft Enamel, in general speaking, it is cheaper in cost compare to Synthetic and Hard Enamel. It has a similar color render to Synthetic Enamel but color zones recess and lower than metal boarders. Metal boarders are easy to define.