There is no need to argue over which of the New Years is the right one. This is a foolish submission to a false choice that is far too pervasive within today's Messianic/Christian theological fringe. Biblically speaking Nisan is the first of months as per the instruction of God Exodus 12:2. This does not negate other beginnings like Tishrei (Ezekiel 40:1). We need not choose one over the other, they both serve God's purposes.
In a figurative sense, I was born of water into this world on the first day of Tishrei and I was born again of the Spirit on the 17th day of the month of Nisan, both are new years, both are beginnings. I refuse to submit to the teaching of those that demand I choose one over the other. I was born a Jew, I am born again a Jew through Yeshua the King of the Jews.
-Yaakov ben Yehoshua