As the Son of Man, he would not be equal to the Father, as he's just a man ("The Father is greater than I" John 14:28). As the Son of God, he has equality with the Father ("Who, though he was in the form of God, did not count equality with God a thing to be grasped" Phil 2:6).
The triune God consists of the Father, Jesus (Son of God), and the Spirit. Only Jesus, has a dual nature (as the Son of Man and Son of God). Prior to his incarnation, Jesus had no dual nature. Neither the Spirit or the Father have dual natures.