The key difference is that the Torah is speaking to the letter of the law, Paul is speaking to what Jesus says of it.
As Jesus says in Matthew 5:
17“Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. 18I tell you the truth, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished. 19Anyone who breaks one of the least of these commandments and teaches others to do the same will be called least in the kingdom of heaven, but whoever practices and teaches these commands will be called great in the kingdom of heaven. 20For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven.
He goes on to give an example:
“You have heard that it was said to the people long ago, ‘Do not murder,a and anyone who murders will be subject to judgment.’ 22But I tell you that anyone who is angry with his brotherb will be subject to judgment. Again, anyone who says to his brother, ‘Raca,c’ is answerable to the Sanhedrin. But anyone who says, ‘You fool!’ will be in danger of the fire of hell.
In the case of the Torah, the requirement is simply to do the sacrifices and not go after idols. It is completely a works based thing.
Paul could, for example, in Acts 23 say:
Paul looked straight at the Sanhedrin and said, “My brothers, I have fulfilled my duty to God in all good conscience to this day.”
but also say, as he does in Romans 7:
14We know that the law is spiritual; but I am unspiritual, sold as a slave to sin. 15I do not understand what I do. For what I want to do I do not do, but what I hate I do. 16And if I do what I do not want to do, I agree that the law is good. 17As it is, it is no longer I myself who do it, but it is sin living in me. 18I know that nothing good lives in me, that is, in my sinful nature.c For I have the desire to do what is good, but I cannot carry it out. 19For what I do is not the good I want to do; no, the evil I do not want to do—this I keep on doing. 20Now if I do what I do not want to do, it is no longer I who do it, but it is sin living in me that does it.
21So I find this law at work: When I want to do good, evil is right there with me. 22For in my inner being I delight in God’s law; 23but I see another law at work in the members of my body, waging war against the law of my mind and making me a prisoner of the law of sin at work within my members. 24What a wretched man I am! Who will rescue me from this body of death? 25Thanks be to God—through Jesus Christ our Lord!
That tension works itself out in the difference between the letter of the law and the spirit.
For Jesus, it is a whole life shift - one that involves regeneration of the mind. To actually put to death the sinful nature is impossible on one's own. To live out the perfection of the law is, as Jesus sets the bar, beyond man's ability.
Just checking off the boxes, as Moses commanded, is a much lower bar indeed.
That said, I'm not sure that in my own power, I would have even met that one.