Plainly, the difference between the old and the new, is the Spirit, the law being the old and the new being the Spirit. Christianity is centred around Christ, so when it says that He became a life giving Spirit, this means that the whole premise of the Christian faith rests on this promised giving of the Spirit to all who believe. This new faith is termed the new covenant or new arrangement with God by which men become acceptable to Him. Since there can be no eternal life without love, and God IS love, then the fruit of the Spirit is mandatory with regard to salvation, because love is a fruit of the Spirit. Therefore plainly, the Spirit is mandatory to salvation also, because it is the instrument of rebirth into the nature of God, by the nature of Christ.
The difference between law and Spirit is the Spirit. You can have all the law you like, but without the Spirit of life there can be no life, not of the eternal kind anyway. The old covenant is not simply one which has been modified by the Spirit, it is one which has been replaced [for Christians*] by the Spirit. The Galatians ran foul of this by trying to retain elements of the old in the new, but they were told that law was equivalent to flesh, because law relates only to flesh and not to Spirit. The old and the new are separated by the spirit of the law, you either have the law as law, or you have the spirit of the law as Spirit, you cannot operate both together, it is the one or the other, they go through different filters. You cannot put new wine in old wineskins, they are incompatible.
Edit update*
CROSSROMAN 
Does ‘The Spirit’ change the Ten Commandments as the morality guidance for the humans?
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Hi Vladimir. Those of the Spirit are of an altered form of consciousness regarding morality, compared with those not of the Spirit. The ‘ten commandments’ presents to human consciousness the reality of the difference between themselves and their behaviour, compared with God and His behaviour. Those of the Spirit recognise this difference and adjust themselves to it by the change that occurs in their conscience when they believe in the forgiveness mercy and love shown by God through Jesus as being the one ordained to fulfill all righteousness on our behalf, so as to give them a new clean foundation on which to build this righteousness within themselves, based on their release from the sin condition and its consequences, so they are free to follow its Spirit which is God’s Spirit as given through the mediator Jesus, from a clear conscience towards righteousness instead of one tainted with guilt. The Spirit is not at odds with the ten commandments, but, being the Spirit of the returned Jesus, is of the same righteousness which the law speaks of and demands, and which He himself fulfilled completely in His own body, becoming also the example and firstborn of perfected humanity, and now Himself the standard of righteousness to be acquired as a gift of righteousness to mankind. In the Christian faith therefore, the ten commandments become that standard by which men recognise their condemnation and the death of their spirit and body because of it. Christianity sees that God has done a new thing (Habakkuk 1:5, Isaiah 43:19, Acts 13:41) by which men can be completely cleansed of their old human ways, and as such, that men are now to live by the standards of the forgiveness which was exercised towards them, rather than by those righteous laws which did not in themselves make provision for the complete cleansing of the conscience towards God. Paul says that the law is good if a man uses it lawfully (1 Tim.1:8), or properly, that is, to show the wickedness of mankind and his need to return to God. That man’s wickedness in the actions he performs are only recoverable through the mercy of God as shown by the complete absolution of sin and sinning, only achievable by the renewing of man’s nature through the revelation of God’s complete and utter mercy towards him through the perfected and risen Christ. The ten commandments are foundational to the confrontation of man with his sin, but once he has been reborn by and into the very nature of God through Christ, he then lives from that new revelation as a means by which he overcomes the old standard of measuring righteousness and its condemnation for the lack of it. He lives from the forgiveness of transgressions of the law and of all unrighteousness, the Spirit of which then becomes his new standard of righteousness by which he is guided, this internalised Spirit being that of the returned Jesus who has gifted His own victorious nature to men who were previously enslaved only to their own natural sinful nature. Jesus who rose from the dead.
Romans 3:31. “Do we then nullify the law through faith? May it never be! On the contrary, we establish the law.” Rom.13:10 “Love does no harm to its neighbour, therefore, love is the fulfillment of the law”. Romans 13:9 “For this, “You shall not commit adultery, you shall not murder, you shall not steal, you shall not covet, and if there is any other commandment, it is summed up in this saying, “You shall love your neighbour as yourself”.
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