Neither one nor the other - so briefly you can answer the question put in the headline. The cross is not an amulet that protects one's presence, or a beautiful accessory, whose purpose is to attract the attention of others. In Christianity, this instrument of execution became the symbol of victory over death. So what is the true purpose of the cross and why do believing people wear it around their necks?
We preach Christ crucified, for Jews the temptation, and for the Greeks madness, for the called ones, Jews and Greeks, Christ, God's power and wisdom of God - so the Apostle Paul speaks of the perception of the Savior's cross death in the company of that time (1 Cor 1 23-24). Crucifixion on the cross was the most terrible, painful and shameful execution in the Roman Empire, because the very form of the cross of the Sign inspired fear and disgust. But everything changed after Christ accepted the sufferings on the cross, and death through death was overcome by his death, rising from the dead. Since then, for all believers in the Lord, the cross became the symbol of this victory and already did not bear the negative significance that was attributed to him before.
Such a transformation of perception was unique. The people around could not immediately accept such changes. The suffering and death of the God-man of Christ was a temptation for Jews who perceive their Messiah as an earthly mighty king. For the Greeks and the carriers of Hellenic culture, it seemed insane that God could be crucified on the shameful cross. However, this crucifixion, sacrifice and death of the Lord made it possible to transform the perception of the cross. As the instrument of the salvation of the whole world, the Cross of Christ was sanctified by God's grace and became a symbol of protection for all Christians from all evil.
In the first centuries, Christians wore crosses of different shapes, according to local traditions, but this did not change the very essence of the sign of the cross. Sometimes the sign of the cross was simply drawn on the forehead or on the chest. Thus, the tradition of wearing the nativity cross goes back to the deep Christian antiquity. 
The naked cross is worn around the neck of a person after holy Baptism, according to the words of the Savior: Whoever wants to follow me, let him deny himself, and take up his cross, and follow me (Mark 8:34). This is done to ensure that the cross is a reminder to a person that he is a member of the Church of Christ, and must walk his life with dignity, remembering that great sacrifice on the cross that Christ brought for him. The sign of the cross also keeps the person carrying it from all evil, but only if the wearer himself does not depart from the fulfillment of the commandments: he regularly communes, does good deeds, turns to God in prayer.
Unfortunately, in the society many superstitions connected with the crosses are common. Often one can hear of a single correct form of a cross, although the Monk Theodore Studite observed in the 9th century that: The cross of every form is a true cross. Also, the material from which the cross is made is not important. It can be precious metals, and a simple tree or a plexus of thread. The nativity cross can be as with a detailed depiction of the crucifixion of Christ, and without any images at all. This in no way detracts from its significance, especially since it was relatively recent to depict on the crucifixes of the crucified Lord.
Buying a cross, it is important to remember that the person who wears it must, first of all, live according to the teachings of the victim of Christ the Savior on the cross, rather than wearing it as jewelry or perceive as a charm. All this has nothing to do with Christianity. In church hymns, the Cross is called the guardian of the whole universe and the defeat of demons, therefore every person worthy of the cross is under the protection of divine grace.
