First, even a cursory reading of both quickly shows that they cannot both be true, because one contradicts the other in very important points.
The Qur'an says the original Scriptures (the Hebrew ones of the Jews, and the Greek ones of the Christians) were perfect when God gave them, but that people corrupted them. Sura 5:13-15 claims:
"But because of their breach of their Covenant [the Jews], We cursed them, and made their hearts grow hard; they change the words from their [right] places and forget a good part of the Message that was sent them... From those, too, who call themselves Christians, We did take a Covenant, but they forgot a good part of the Message that was sent them: so We estranged them, with enmity and hatred between the one and the other, to the Day of Judgment... O People of the Book! There hath come to you our Messenger [Muhammad], revealing to you much that ye used to hide in the Book, and passing over much [that is now unnecessary]: there hath come to you from Allah a [new] light and a perspicuous Book.."
This is terribly convenient for them when they come across Hebrew and Greek Scriptures that are at odds with their Qur'an, you see. They can claim that those bits are later corruptions, and that the Qur'an is the new light that is uncorrupted. This means that anybody believing the Bible to be the Word of God must be made by Muslims to see the error of their view and submit themselves only to what the Qur'an says. Yet the Jesus of the Qur'an is not the Jesus of the Bible. The Qur'an only has 25 verses mentioning Jesus! What is anybody going to learn about Jesus from such meagre mention?
If you want to know about Jesus, read the Bible, for He was prophesied to come as the Messiah in the Old Testament, and the New Testament is full of what He said and did, and how He truly is the Son of God, crucified and resurrected, which the Qur'an denies.