Thank you for your interesting question. Not one I have ever really thought on. First off, I don’t know if Satan understands a deeper level of evil than is possible for humans, but he certainly seems to have more power to effect evil out-workings upon the earth than what humans can. To your question on why is Satan so evil, it is a question not so much on what evil is but rather on the degree of it.
Scripture says that God is love (1 John 4:8), and therefore God’s nature is that of love. The opposite of love is not hate but selfishness. The less we love the more selfish (self-seeking) we become. So for Satan, as for humans, the more selfish we are the less loving we are and therefore the more evil we become in our nature. In the case of Satan, not only does he desire to be God, he even desires God to bow down and worship him.
Matthew 4: 8-10:
Again, the devil took him to a very high mountain and showed him all the kingdoms of the world and their glory. And he said to him, “All these I will give you, if you will fall down and worship me.” Then Jesus said to him, “Be gone, Satan! For it is written,
“‘You shall worship the Lord your God
and him only shall you serve.’”
This is a staggering passage of scripture. Satan is asking the One by whom and through whom he was created, the most supreme being in existence, to lie prostrate before him and worship him. Audacious isn’t the word. I think this pride or selfishness to try and elevate yourself above God, and actively work to do so, is one way in which it leads to a ‘worse’ evil.
This also speaks into our own personal lives in that we must also surrender our lives and wills daily over to God and make sure He is first in our lives.
I hope that is of some help .