Muslims have a major dilemma on their hands. In both the Qur'an and the Haddith, the Bible is held in high regard. Muhammad paid all kinds of lip service to the Judeo Christian God, and even to this day, his religion is classified as "Abrahamic". The problem? The Bible does not respond in kind. Whereas Islam praises the Bible, the Bible utterly refutes Islam. In Islam, God is no father, but in Christianity, God is our Heavenly Father. In Islam, Jesus is the son of Mary, but not the Son of God. In Islam, Jesus will testify that He never commanded Christians to take Himself and Mary as gods besides Allah, yet in Christianity, while Mary certainly is not the object of worship (Muhammad didn't understand half the things he criticised), Christ Himself is God. I could go on. Biblically speaking, Allah is a false god, Muhammad is a false prophet, Islam is a false religion, and Muslims need to repent, lest they be condemned.
So what's the solution to this? The one argument Muslims use today is that the Bible has been corrupted. The Bible we have today is, according to Muslims, not the same as it was during Muhammad's life. Now, this is actually a very easy claim to refute even from the Qur'an. It's simple logic really: The Qur'an affirms that the Bible is the word of Allah, the Qur'an affirms no one can corrupt his words, the Qur'an therefore denies the possibility of the Bible being corrupted. However, this is low hanging fruit. It is perhaps more helpful to show that, whereas the Qur'an has historically been in a position for corruption, this was never the case for the Bible.
See, the Qur'an, according to Islamic sources, has not survived well at all. Much of it has been lost, such as "the verse of stoning and breastfeeding an adult 10 times", which, in Sunan Ibn Majah 1944, Muhammad's wife Aisha informs us no longer exists, because she kept the only copy under her bed, and while she was preoccupied with Muhammad's death, her sheep broke in and ate it. This verse remains absent from the Qur'an to this very day. This is far from the only problem that occurred with the Qur'an after Muhammad's death. In fact, long story short, a man named Uthman compiled the Qur'an to the best of his abilities (much to the chagrin of many Muslims in his day), and burned whatever else he could find.
This is rather embarrassing compared to the Christian scriptures. See, there has never been a central authority in Christianity. In the beginning, congregations acted largely independently. When new scriptures were revealed, they were copied, they were circulated, they were scrutinised, they were finally accepted. By Muhammad's time, those scriptures had been circulated so far and wide that even if we had our own "Uthman", his mission to destroy all versions different from his own would fail miserably. Supposing he started in Arabia. How's he going to corrupt the copies in Egypt, or in Rome, or anywhere else where a congregation had been established? It wouldn't be possible. We even have some manuscripts from before Muhammad's time that affirm the Bible we have today is the same as in the past.
So, has the Bible been corrupted? Far from it. Any attempt to do so would fail miserably. By contrast, much of the Qur'an was lost after Muhammad's death, and many disagreements arose. These disagreements were "solved" by Uthman, who compiled the Qur'an we have today, and burned all the disagreeing copies he could get his hands on. In other words, ironically, the Qur'an, not the Bible, was corrupted, and by Muslims at that!
But ultimately, it is not the corruption of the Qur'an that Muslims need to worry about. Rather, it is the corruption of the soul. See, both Christianity and Islam teach that we are all sinners, and deserving of Hell. However, whereas in Islam there is no clear plan of salvation, Christianity presents one. Just one. While Islam claims Jesus was never crucified, He actually was, and in doing so, He received in Himself the full wrath of God for sin. All who confess Him as Lord, and believe He rose from the dead, will receive eternal life. Which prophet would you rather put your faith in? The one who conquered death, or the one whose own religion fell into chaos after his?