The Sun does not destroy the Moon but when it rises the Moon passes away.
I will answer this question from a Covenant Theology standpoint.
The law is commonly divided into ceremonial, moral and civil.
In Christianity it is agreed by most that Christ fulfilled the meaning of all that was ceremonial and that therefore when the curtain of the temple was torn from top to bottom these laws became 'obsolete'. From this standpoint all ceremonial laws, of which the High Priest offering sacrifices in the temple were probably the most sacred, are no longer application by obsolescence.
In the same manner most Christians believe that the civil laws that were used to govern Israel, such as the many capital punishments by stoning, burning, or strangulation ceased. These are also viewed as being symbolic of man's need for salvation under the 'curse of the Law'. Also as the invisible church of Christ replaced the literal outward church of the Jews, God no longer directly governs the Jewish people. There are some Christians who still think that God in some way governs the Jews. (I think dispensationalists still hold some ideas about this but am not sure of the details, as I am not that familiar with this unique view).
The controversy is mostly about how God’s moral law in the Old Testament should be applied today, or if there is any change to it at all. Most Christians who propose the idea that 'nothing changed' to God’s moral Law at all in Christ’s death, commonly refer to this verse where Jesus said:
"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. (NIV Mathew 5:17)
A common verse referred to by those that believe the entire Law (moral, ceremonial, civil) was 'nailed to the cross', so that even its moral nature was modified in Christ, commonly refer to the verse:
For the law was given through Moses; grace and truth came through Jesus Christ. (NIV John 1:17).
Even among traditional reformed theologians many are divided over this question about the moral law. I am of the camp that you can’t divide the Law at all, so that all aspects were fulfilled in Christ and so nothing remains exactly as it was. For example, the Law said we should love our neighbor as ourselves, however it did not provide any ability to do so but condemned to hell any offence. In Christ however, under the liberty of grace, a stony heart has been replaced by a soft one, and an uncircumcised heart has been circumcised, therefore, Christians have love in the heart and can follow the command. Therefore, even the moral law has not gone un-crucified as it was formerly written on stone but now in a 'Spirit of liberty' it is written in a believer’s heart. In this way, Christ abolished even the moral law in the sense that he fulfilled all its requirements and then imputed that righteousness to believers, which in turn, infused the holiness required by the law as a basic 'principle of life and liberty' into Christians. In this sense the Bible say’s we are ‘no longer under law' (that is the moral law).
For sin shall not be your master, because you are not under law, but under grace. (Romans 6:14).
This last verse I quote is at the heart of the debate for depending on which theologian you consult the moral law is intended, or not intended, by this and similar verses. As for me I am absolutely convinced the moral law is chiefly intended as described above. Here are some reformed theologians who share my view. There are other theologians who do not but I am not bothering to represent them, as I find their position unscriptural:
The law of Moses was, in the first place, a re-enactment of the covenant of works. A covenant is simply a promise suspended upon a condition. The covenant of works, therefore, is nothing more than the promise of life suspended on the condition of perfect obedience. The phrase is used as a concise and convenient expression of the eternal principles of justice on which God deals with rational creatures, and which underlie all dispensations, the Adamic, Abrahamic, Mosaic and Christian. Our Lord said to the lawyer who asked what he should do to inherit eternal life, “What is written in the law? How readest thou? And he answering said, Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy strength, and with all thy mind; and thy neighbor as thyself. And he said unto him, Thou hast answered right, this do and thou shalt live,” Luke 10:26-28. This is the covenant of works. It is an immutable principle that where there is no sin there is no condemnation, and where there is sin there is death. This is all that those who reject the gospel have to fall back upon. It is this principle which is rendered so prominent in the Mosaic economy as to give it its character of law. Viewed under this aspect it is the ministration of condemnation and death. ( Hodge 2 Cor P75)
Jonathan Edwards –
Jonathan Edwards also sees the Mosaic covenant as being different from the gospel as it includes the renewal of the covenant of works that has the ministry of death and cursing, leading sinners to Christ as a harsh schoolmaster.
As the law was given at Mount Sinai, so Christ delivered his evangelical doctrine, (full of blessings, and not curses,) to a multitude on a mountain. Matt. v.— (Jonathan Edwards History of Redemption, P302)
I think really that the covenant that God made with the children of Israel was the covenant of works. He still held them under that covenant; that is, what is required in that covenant is to them particularly deciphered, and many additional positive commands which answer to the precept concerning the forbidden fruits and God proposes this covenant to them as the condition of his favor, and gives them to understand that none of those promises he had made could be challenged without perfect obedience: but yet gives them to understand so much of his merciful nature and his inclination to pity them and to accept of a propitiation for them, that they, finding that they could not challenge anything from those promises [on the ground] of obedience, trusted only to the mere undeserved mercy of God and were saved by grace, and expected life only of mere mercy.
We are indeed now under the covenant of works so, that if we are perfectly righteous we can challenge salvation. But herein is the difference betwixt us and them: to us God has plainly declared the impossibility of obtaining life by that covenant, and lets us know that no mortal can be saved but only of mere grace, and lets us know clearly how we are made partakers of that grace. All ever since the fall were equally under the covenant of grace so far, that they were saved by it all alike, but the difference is in the revelation: the covenant of works was most clearly revealed to the Israelites, to us the covenant of grace. The church, which was then in its infant [state], could not bear a revelation of the covenant of grace in plain terms; and so with them the best way to bring them off from their own righteousness was to propose the covenant of works to them, and to renew the promise of life upon those conditions. God did with them as Christ did with the young man that asked what he should do for eternal life: Christ bids him keep the commandments. And in that sense they were under the covenant of works, that it was proposed to them as the condition of life, that they might try. To us it is not so. The covenant of grace was indeed insinuated to them and proposed under covert, but 'twas to that they were all forced to fly. The promises seem to be so contrived as to give them to see that they can't challenge anything except they perform a perfect obedience, if God will be strict, but yet that he will of his mere mercy accept them into his favor if they perform a sincere obedience proceeding from the true love and fear of him; so that the fruits of faith are proposed instead of faith itself. But by this, none but such as had faith could hope for life; and by God's contrivance of that dispensation they were led not to depend on these as works, but as a disposition to receive, as so many manifestations of repentance and submission; and they depended on them as such only, for life. (Jonathan Edwards. The "Miscellanies". Page P363-363)
With reference to what has been before spoken of the covenant [No. 2]. Covenant is taken very variously in Scripture, sometimes for a divine promise, sometimes for a divine promise on conditions. But if we speak of the covenant God has made with man stating the condition of eternal life, God never made but one with man to wit, the covenant of works; which never yet was abrogated, but is a covenant stands in full force to all eternity without the failing of one tittle. The covenant of grace is not another covenant made with man upon the abrogation of this, but a covenant made with Christ to fulfill it. And for this end came Christ into the world, to fulfill the law, or covenant of works, for all that receive him....
To say that the covenant of works did admit of a mediator, is something improper. The covenant of works mentioned nothing about it; (Jonathan Edwards. The "Miscellanies". Page P217)
John Owen –
As usual John Owen teaches with the utmost clarity on the subject:
By the sanction of the law, we intend the promises and penalties wherewith by God the observation of it and obedience unto it was enforced. This the apostle hath respect unto in sundry places of this Epistle; the principal whereof are reported in the following dissertation.
To represent this distinctly, we may observe that the law falls under threefold consideration; — first, As it was a repetition and expression of the law of nature, and the covenant of works established thereon; secondly, As it had a new end and design put upon the administration of it, to direct the church unto the use and benefit of the promise given of old to Adam, and renewed unto Abraham four hundred and thirty years before; thirdly, As it was the instrument of the rule and government of the church and people of Israel with respect unto the covenant made with them in and about the land of Canaan. And in this threefold respect it had a threefold sanction. (Owens Works, Volume 17, P654)
Martin Luther –
Martin Luther never prances about with constant distinctions around words, pretending to believe something he does not, he just lays it all out there:
Who would ever believe that these things could be mixed up so easily? There is no one so stupid that he does not recognize how definite this distinction between Law and grace is. Both the facts and the words require this distinction, for everyone understands that these words “Law” and “grace” are different as to both denotation and connotation.62 Therefore it is a monstrosity, when this distinction stands there so clearly, for the papists and the fanatics to fall into the satanic perversity of confusing the Law and grace and of changing Christ into Moses. This is why I often say that so far as the words are concerned, this doctrine of faith is very easy, and everyone can easily understand the distinction between the Law and grace; but so far as practice, life, and application are concerned, it is the most difficult thing there is. (Luther's Works Vol 26, P143-144)
Now the first sermon, and doctrine, is the law of God. The second is the gospel. These two sermons are not the same. Therefore we must have a good grasp of the matter in order to know how to differentiate between them. We must know what the law is, and what the gospel is. The law commands and requires us to do certain things. The law is thus directed solely to our behaviour and consists in making requirements. For God speaks through the law, saying, “Do this, avoid that, this is what I expect of you.” The gospel, however, does not preach what we are to do or to avoid. It sets up no requirements but reverses the approach of the law, does the very opposite, and says, “This is what God has done for you; he has let his Son be made flesh for you, has let him be put to death for your sake.” (Luther's Works Vol 35, P162-164)
Conclusion: The Law can't be divided, therefore when the Law was nailed to the cross all aspects of its were made obsolete not by being destroyed but by being fulfilled in Christ. Christ fulfilled all the ceremonial laws that prefigured him. Christ fulfilled all the civil laws that symbolized the punishments due to sin for which he suffered and was hung on a tree being cursed. Christ fulfilled all the righteous requirements of the moral law becoming sin for us that we would become the righteousness of God by faith apart from any works of our own. This righteousness imputed to us reconciles us to God that we may live holy and obey all the precepts of the Law wich is to love God and your neighbour in many good works. In this sense Christ fulfilled all the Law and there is no reason to split the law where the Bible does not.