Indeed - one finds throughout the New Testament direct references to the Old Testament passages, both in the Law and the Prophets, not only spoken by Christ but by the apostles as well. The New Testament is confirmed by the Old Testament. By contrast, the Koran rarely makes direct reference to the Old Testament or New Testament except through vague names and ideas.
Mohammad taught at one point that Jews and Christians should look to their books to verify who he was, but then later on (obviously when he found out what those books really said) claimed they corrupted their scripture and hid the truth. Hence Muslim apologetics today are left with a circular logic where anything that supports their cause is used as God’s word yet anything that contradicts the Koran is untrustworthy - in other words, I agree with it because it fits my personal theology. One must ask why, after thousands of years, did God change from having His revelation be confirmed by the previous revelation to sending down a book which all books thousands of years before have to coincide with?
In regards to the Torah and koran, one big argument that I’ve heard from both the Koran and Muslims is the overemphasis on Ishmael, the ancestor of the Arabs whom Muslims believe to be part of the covenant with God. What they forget, however, was that Ishmael’s birth was a human plan (Sarah had Abraham sleep with a slave)
But God said, "No, but Sarah your wife will bear you a son, and you shall call his name Isaac; and I will establish My covenant with him for an everlasting covenant for his descendants after him. “As for Ishmael, I have heard you; behold, I will bless him, and will make him fruitful and will multiply him exceedingly He shall become the father of twelve princes, and I will make him a great nation. But My covenant I will establish with Isaac, whom Sarah will bear to you at this season next year.” [Genesis 17:19-21; emphasis mine]
God looked after Ishmael out of mercy - it ended there. The covenant and the promise of mankind’s salvation came through Isaac and eventually Jesus Christ.