That is something that I can’t answer. I just know that Variety 1 is the no shield with a Laurel wreath while Variety 2 is the Oak Wreath with a shield. Both of those are copper-nickel compositions. Variety 3 is Bronze and was produced due to the copper-nickel cents disappearing from circulation due to the civil war.
From what I have read the Mint Director, James Ross Snowden, wanted the design changed at the time for unknown reasons. He asked designer, James Longacre, to make the change. As for the change in composition from copper-nickel to bronze, that was probably a cost saving measure. The Congress and the mint saw that people were willing to use the, lighter Civil War tokens, which were mostly made of copper or bronze, and picked up on that idea. The bronze cents were lighter in weight, and the metal is easier to work with. Nickel has a higher melting point, and it is hard and brittle. The mint employees did not like working with it. They called nickel "the devil's copper."