It does not matter whether Christ refered to himself as Son of God or Son of Man, both cannotate the same thing. More precisely the most semitic sayings in nature in the synoptics, Christ refers to himself as "Son", such as the saying, "No one knows that hour not the angels in heaven nor the Son but only the Father."
Christ many times made a distinction between "my God" and "your God" or "My Father" and "Your Father". In order to demonstrate a difference between his relationship with God from ours. In Christ's prayer life he refered to God as "Abba" (literally papa or daddy). Christ spoke of God in a direct familial way, as that of a child to his parent, this is quite unique. The internal evidence of the text further demonstrates that very early it was common to associate Christ as the "Only/Beloved Son". Christ makes mention of this about himself as the Only/Beloved Son in a parable, "Therefore having one Son His Beloved , he also sent him to them last saying, They will respect my son...(Mark 12.6).
This close relationship in a direct way as the Father being a literal daddy to Jesus conveyed the idea that Christ was indeed divine and did indeed have a personal relayionship as a son to a father. It even raised the ire of hs fellow jews, "Therefore the jews sought all the more to kill him, because He not only broke the sabbath, but also said that God was His Father, making himself equal to God."(Jn 5.18)
This close relationship using the "beloved/only" title is echoed in the divine voice emanating from heaven, "This is My Beloved Son in Whom I am well pleased..."(Mk 1.11).
In the epistle to the Colossians it reminds us not about the Son of God(or man) but as it says, "He has delivered us from the power of darkness and conveyed us into the Kingdom of the Son of His Love".(Col 1.13)
A semitic saying relating Christ as a Son of the Father is found in Matt 11.27 where Jesus says of himself-, "All things have been delivered to me by My Father, and no one knows the Son except the Father. Nor does anyone know the Father except the Son, and the one to whom the Son wills to reveal him".
The above saying is mirrored in the gospel of John which is closely related to the "only/beloved" lineage of the Son title, "No one has seen God at anytime, the Only-begotten Son who is in the bossom of the Father has declared Him."(Jn 1.18)
All these sayings demonstrate the exclusiveness of the relationship between God and Christ which differs from the norm.
Lets now take a look at a title never used by Christ for himself in the NT, nor by his disciples, and never was part of the christian tradition at anytime, yet played an important role in the last days of Jesus life. That of "King of the Jews". This was one of the charges brought againt Jesus during his trial. In fact it was so prevalent that it was written in 3 different languages over the cross. When the jews read the inscription, "Jesus of Nazareth, the King of the Jews" over his cross, they quickly asked the roman authorities to change it, to read: "He said I am the King of the Jews".(Jn 19.19-21)
By the time Christ was crucified the claim of being a King and being a Son of God implied the same thing which is messiahship, the one the jews awaited for.
"And they put up over his head the accusation written against him" This is Jesus the King of the Jews.....and those who passed by him blasphemed him, wagging their heads saying, "You who destroy the temple and rebuild it in three days, save yourself, If you are the Son of God, come down from the cross. Likewise the chief priests also mocking him with the elders said, He saved others, Himself he cannot save, If he is the King of Israel, let him now come down from the cross... He trusted in God, let Him deliver Him now if He wiil have Him, for He said I am the Son of God ". (Matt 27 37-43)
As we can see from the above passage "Son of God" and King of the Jews (or Israel) was interchangeable. In Matthew's gospel Christ asks his disciples who do people claim he is. After the disciples respond, Christ then asks them who they say He is. Peter answers, "you are Christ the Son of the Living God"(Matt 16.16) Jesus them exhorts him that it was God who revealed this to him not man.
This parallels the conversation Jesus had with Pontius Pilate. "Then Pilate entered the Praetorium ,called Jesus and said to him, "Are you the King of the Jews"? Jesus answered him, Are you speaking for yourself about this OR did others tell you this concerning me?" (Jn 18.33-37)
The title Son of God is actually the less prestigious title in the gospels. On the otherhand the title Son of Man is of a higher christological value. To demonstrate this lets look at when the chief priests interrogate Christ, "Are you the Christ the Son of the Blessed?, Jesus Answered, I am and you will see the Son of Man sitting at the right hand of the power, and coming with the clouds of heaven."(Mk14.61)
Here we have recorded a highly semitic saying where even the name of God is avoid being mention as was customary among the jewish culture. The Chief priests tore his garment and the sanhedrin proceeded to convict him to death.
Now lets take a look at the only time in the entire NT where someone uses the title Son of Man for Christ rather than Son of God, "But he being full of the Holy Spirit gazed into heaven and saw the Glory of God and Jesus standing at the right hand of God, and said, Look! I see the heavens opened and the Son of Man standing at the right hand of God! Then they cried out with a loud voice, stopped their ears ad ran ay him with one accord. and they cast him out of the city and stoned him...(Acts7.55-58)
As we can see, the jews wanted death only when either Christ himself or a disciple made Him on par with God. The title "Son" (of God or man) can be used interchangeably in the NT and Son of Man in the synoptics tends to be the more prestigious title.