How much of the Law of Moses still applies? First we must understand why we have the Law. Originally, the only rule was to not eat from the fruit of the knowledge of Good and Evil (Genesis 2:17). Then what followed because that happened. Cain killed Able (Genesis 4:8). Then eventually the flood. The answer is found in the reason for the flood. "The LORD saw how great the wickedness of the human race had become on the earth, and that every inclination of the thoughts of the human heart was only evil all the time. (Genesis 6:5)"
So God's desire can be explained in the inverse: "God would see it great if the human race was kind on the earth, and that every inclination of the thoughts of the human heart was only good all the time."
This idea is also proven by Jesus himself: Jesus said to him, “‘Love the Lord your God with all your heart, with all your soul, and with all your mind.’ This is the first and greatest commandment. The second is like it: ‘Love your neighbor as yourself.’ All the law and the prophets depend on these two commandments.” -Matthew 22:37-40
The description of kindness and good thoughts of a human heart: If you where set to the task of ruling people toward God's desire. What might you put on your list? (Ok, nobody kill each other, don't steal, etc.)
Why the List didn't work? Pride, Ego, Natural Rebellion (Simply because the list exist).
How Faith leads to kindness and good thoughts and replaced the list. If you want people to have good thoughts about each other. More analysis needs to be focused on what makes people have bad thoughts. If you could stop the bad thoughts, then you have a world of only good thoughts. Lets take a look at psychology and pinpoint what causes anger. What we find is that anger is caused by the decision to fix the threatening behavior. So if we never took negative matters into our own hands, and relied only on God to justly handle the situation. We can prevent ourselves from getting angry.
Does this ideology match with the teachings? Do not take revenge, my dear friends, but leave room for God's wrath, for it is written: "It is mine to avenge; I will repay," says the Lord (Romans 12:19). But I tell you, do not resist an evil person. If anyone slaps you on the right cheek, turn to them the other cheek also (Matthew 5:39). But now ye also put off all these; anger, wrath, malice, blasphemy, filthy communication out of your mouth (Colossians 3:8). When they kept on questioning him, he straightened up and said to them, "Let any one of you who is without sin be the first to throw a stone at her." (John 8:7)
What evidence do we have that God will take care of it for me? When they began to shout and praise, the Lord suddenly attacked the Ammonites, Moabites, and men from Mount Seir who were invading Judah, and they were defeated (2 Chronicles 20:22).
Oh so the Law is still active? Yes (Luke 16:17).
Oh so God fulfills the law! Yup, if someone cuts out my eye, if God feels that it is necessary, he will cut that eye out for me. This is done so that my thoughts are "good" and that "evil can avoid my heart".
Now what if everyone followed the Law But everyone didn't. "When Jesus went outside, the Pharisees and the teachers of the law began to oppose him fiercely and to besiege him with questions," (Luke 11:53). The outcome of the law and the thoughts in their heart.
So the Law is inferior to faith? Yes, because it didn't accomplish God's Desire.