First: What we know of Socrates comes from the works of his student Plato. The earliest copies, seven total, of Plato’s work comes from over 1,000 years after Plato died. Similarly what we know of Jesus was recorded by his followers but we have far more copies dating back to the lifetime of the eye-witnesses.
The earliest copy from the gospels is a fragment of John’s gospel from within 100 years (at the latest) of when it was originally written. There are over 5,000 ancient fragments and manuscripts for the New Testament that record the life, teachings, and influence of Jesus, making the New Testament the most widely evidenced work of all of antiquity.
Second: Socrates did not die claiming to be God. One of the accusations against him was atheism, which was not because he did not believe in a god, but because he rejected the notion of the multitude of Greek gods (polytheism). If you read Socrates’ “Apology” (written by Plato) you will see that he professed belief in one God, a monotheistic view as opposed to to the polytheistic view of his culture.
Jesus made many claims to be God and performed miracles to authenticate his claim. He claimed to the be the fulfillment of the Old Testament prophecies that God would send a Messiah. His crucifixion was a result of such claims. Though both died for their beliefs, one a belief in monotheism and one for claiming to be God, their deaths, in and of themselves, do not really settle the argument.
Third: Socrates is still dead. He died by drinking poison called hemlock. Jesus, on the other hand, rose from the dead, according to the Scriptures. He was seen after his resurrection by many eye witnesses as recorded in the gospels of which we have thousands of copies, some dating back to the lifetime of the eye-witnesses.
While the first two points are interesting, the last one pretty much closes the case. Socrates vs. Jesus: no contest. Mic drop.
By the way, a fun read that deals with this question (in a very general sense) is Peter Kreeft’s book “Socrates Meets Jesus: History’s Greatest Questioner Confronts the Claims of Christ.”