Holy Exegesis Batman!

As I've done textual work on both, I'll offer some observations.

First and foremost, the Qur'an as it is known today was not written down until after Muhammad died. If it was written down, there would be no need for those fantastically talented men who've earned the title of Hafiz! A Hafiz is someone who has memorized the Qur'an in its entirety. You can give them the number of any verse and they will recite the correct verse back to you in beautiful medieval Arabic. Verbatim. Although it is written down, it's meant to be recited. In fact, Qur'an is a verbal noun of qaraʾa which means "he recited". How fitting!

Second, I'll offer a different viewpont of thinking about the Qur'an and the Bible. In Christianity, Christ is said to be 'The Word of God made Flesh." While the Bible contains the Word of God, the book itself is not 'The Word of God." Christ is. In Islam, the Qur'an IS the 'Word of God'. The physical object and contents are one in the same. Therefore, it is more analogus to compare Christ to the Qur'an, than to compare the Qur'an and the Bible. The two texts are similar in that both are available from your local book retailer in either hard or soft cover. That's it. The Qur'an does retell stories that are found in the Bible and Old Testament, and certain imagery and word phrases are repeated through all three, so it is possible to compare those specifics. However, any comparisons beyond that are highly problematic.

Third, to be perfectly honest Christians have been called both dhimmi (People of the Book) and kufir (Infidel). That in large part depends on a little known principle called naksh, or abrogation. Naskh is a highly controversial technqiue that has been applied sporadically and unequally throughout Islamic history, and is a method of determining which source will be applied in cases where the Qur'an and the Sunnah conflict (which is often). Unless you're up-to-date on your tafsir and history of each verse, to include its isnad, chain of transmission, it can be like attempting to naviagate a minefield blind-folded.

Fourth, comparing Islam and Christianity- or any two religions, is a broad topic. So broad, Comparative Religious Studies is a field unto itself and scholars focus specifically on a particular point of commonality. If you have questions, I'd be glad to try and answer them, but you've got to give me something more specific to work with or else you're going to get a very general answer.