Theogony and Genesis chapter 1, have many differences. In each piece of literature, we see the foundational concepts of two completely different worldviews. The entire system of ethics, hierarchy, and sanctions is completely different.
Theogony was a poem written by the Greek poet Hesiod (c. 750-650 B.C.). He began with his account on the Muses, 9 goddess daughters of Zeus and Mnemosyne. These Muses told him to sing of the races of the gods, and that is what Theogony is fundamentally about.
It was believed that chaos came to be, however we are not told how. From this chaos, came Earth, followed by the gods she bore and their descendants. The creation came about by means of sexual relation between the gods.
It is evident from this poem that the gods did not have a consistent system of ethics and sanctions. The curses brought on man were not a result of the sins of man. Sanctions were also imposed on the gods, however theses were also inconsistent, because there was no real system of ethics.
It is not said in Theogony, where men come from. They were in a sense, just assumed into the text. It is also apparent that Zeus, who is said to be the most powerful of the gods was not omnipotent. He calls on the other gods to assist in the war against the Titans. He is at the top of the hierarchy, but he is not sovereign over the creation.
In Genesis chapter 1, it is apparent from the first verse, that God is an omnipotent being. He always was, and always will be. Christians believe that God created heaven and earth. He did not make heaven and earth, he created heaven and earth; he started with nothing, and with nothing brought forth the creation. After each subcreation, God saw that it was good and continued. God created day and night to separate the light from the darkness. “God called the light ‘day,’ and the darkness He called ‘night.’ thus evening came and morning followed–The first day” (Genesis 1:5) With each day he brought forth a new creation. On the sixth day of His creation, He created man in his own image and likeness, he gives man a woman as a companion, and He tells them to go forth and multiply.
We cannot fully understand the concept of creating something out of nothing, it is beyond the human mind. However, in Theogony, we are not provided with the origin of men. Were men believed to have been created by the Greek gods? We are not given an answer in this account.
While it is not included in Genesis 1, we see pretty early in the book of Genesis that God lays down a system of ethics and sanctions. Sanctions are imposed based on ethics and it is a consistent system. We do not find that in Theogony, it is evident that sanctions were imposed, but the system of sanctions was not consistent. It was provided in Theogony that the curses man endure existed before man as a result of the behavior of the gods.
These are two completely different perspectives that disagree with each other on many terms. They are completely separate worldviews, that are mutual in very few aspects.