They were cousins, born to Godly parents, and both were predicted in the OT. They both were baptized, were teachers of the Truth, and neither felt the need to abide by all of the regimented Jewish traditions, although each was born Jewish. All of these similarities fulfilled prophecy and brought the Good News to Jews and Gentiles alike.
Jesus and John have special circumstances (miraculous) births. Elizabeth is beyond child bearing age when she becomes pregnant and Mary is not sexually involved with a man when she gives birth. Both John and Jesus preach about the kingdom of God. John’s call to repentance and baptism is in preparation for Jesus’s call to believe in Him as the Son of God in order to be received into that kingdom.
They both fulfilled prophecy. They were cousins. They both proclaimed repentance. They both baptized; John with water and Jesus with the Spirit. Both of their births were announced by an angel. This is significant because they were clearly anointed by God and had a specific part to play in God’s purpose.
The parents had visions, their births were prophesied and their moms were related.
The similarities of Jesus’s birth and John’s birth are abundant. Both are born unexpectedly to mothers and fathers who were blessed by angelic visitation. Both births are miraculous, but one actually presents difficulty to the parents, the unwed Mary and adopted father Joseph, while the other set of parents feels that their prayers for a son have been answered after Elisabeth was thought to be barren. Some have focused on Mary’s virginity as the most significant aspect of Jesus’s birth, but I think the fact that Elisabeth is filled with joy, while Mary is filled with fear is a significant part aspect of the connection between Jesus and John. Jesus is more than a simple prophet and the burden of bearing Jesus is more than just joy. It begins with sacrifice and joy blooms from that sacrifice. Mary knew this reality well and voiced it in the Magnificat. Another parallel that I found fascinating, and never realized before, is that Jews had used baptism as a marker of conversion into Judaism even before John the Baptist. That is significant because John’s baptism marked a conversion, of sorts, toward the fulfillment of the Law. Then, Jesus accepts John’s baptism for himself and connects himself to this “conversion.”
When comparing the births of John the Baptist and Jesus, Luke makes clear that both had mothers that experienced visits from angels with the good news that they would be blessed with pregnancies. Additionally, they were both due to be born around the same time and are cousins by relation. These are significant in demonstrating that they have a close relationship and connection even before they were actually conceived and born. It explains much of why Jesus was so connected to John’s ministry and why it was indeed John who baptized Jesus later down the line.
In the book of Luke, The births of John the Baptist and Jesus are paralleled by the author. Luke emphasizes the miraculous foretelling of John the Baptist’s birth by the angel that speaks to Zechariah. In the same way, Mary and Joseph are both visited by angelic beings with a message of hope and a pregnancy of the Holy Spirit in Mary. It also is emphasized that these two men were cousins, something we don’t necessarily see in the other gospels. Mary and Elizabeth are related and spend time together before the birth of their sons.