The 10 are presented to a post-exodus Israel and establish a covenant relationship. They are framed in a way for a specific time, place and people and we shouldn't expect them to be universal as they were never presented that way. We cannot superimpose the 10 over Christian living and expect the same results because we are not in the same conditions the 10 were made in. The 10 have monotheistic claims and moral pillars framed in a way that uniquely challenges Israel and the surrounding cultures (through Israel). In the NT Christ reframes these as a heuristic approach over a list of dos and donts that is often summed up by NT authors as "loving your neighbour as yourself,"; this is known as "Christ's law".
It is this law that is fundamental and reaches deeper than the 10 can ever. First, "You shall love the Lord your God with all your heart,” this includes the monotheistic claims of the 10 but also far greater. it is not only about idolatry, graven images and using his name in vain (which of course are not consistent with loving God with all your heart), but also innately our every action as directly involved with obedience to love God. Christ calls this the greatest commandment. The second is to love your neighbour as yourself. and this certainly includes not murdering your neighbour, stealing, lying, sleeping with their wife, etc... but it goes far deeper. We are no longer merely resisting doing harm, but Christ flips it and tells us we should be actively seeking to love others.
The 10 simply do not go to this length, and I may keep the 10 but hate my neighbour (and yes, even hate God), which is inconsistent with Christ's law. We cannot approach Christ if we cannot seriously approach our own actions critically to align with Christ. Christ's law has this goal, where the 10 are lacking, and we can keep the 10 while failing to critically address sin in our lives. This is the conversation Christ has with the Pharisees; it wasn't about how well they kept the law, Christ was more interested in their heart. The heuristic approach in Christ's law is not about a check list, and we must actively participate in understanding how our actions contribute to loving God/neighbour.
In its day the 10 were radical claims and ways of thinking challenging not just Israel but surrounding cultures too as a polemic to show order and restoration under God, but Christ's goes deeper than the 10 ever can; He is interested in letters of not just "the heart" but "OUR heart" which is the place where the value is birthed, but he is not interested in the letters on stone which can be exploited to support our own sin and may be devorced from our heart. It is good to think that murder, adultery, stealing, etc... are wrong but most (if not all) would accept this throughout all of civilization without any prompting and the 10 do not hold dominion over these moral claims. It is better to cut to the heart over a motivation to resist evil (which is limited, especially when condensed to 10), but actively be involved with doing good in all our actions. Christ himself tells us "it is lawful to do good on the Sabbath" (Mat 12:12), establishing that goodness itself is above sabbath law (directly) but also more broadly is a comment on all law and a nod to his own commandment that is Christ's law. This focus you will find is far more consistent throughout the NT.