The similarities between the Koran and the Bible lie in the fact that each of these books is considered to be holy scripture for the religion which each represents. The Koran is the holy scripture for Islam and the Bible is the holy scripture for Christianity. Within each of these respective religions, these holy books act as written tools for those who believe, containing what followers would claim as "truth," general guidelines for morality, history of the religion itself, prophesies, and a plan for salvation. The religions themselves are similiar in that they are monotheistic religions (each claims that there is only one God).
The differences between the Koran and the Bible are as vast as the differences between the religions themselves. At the core, the biggest difference lies in the claim of who is Jesus Christ. The Christian Bible essentially is, from start to finish, thematically centered on Jesus Christ as the manifestation of God himself, who came to earth as a man, died, and was resurrected after three days, for the forgiveness of human sin and salvation for all who believe. The principle character of the Koran is not Jesus Christ (though he is considered to be a prophet), but rather Mohammad. Muslims consider Mohammad to be the prophet to whom Allah (God) solely revealed his word. The Koran was then written by followers of Mohammad.
Stylistically, the two books are also very different. The Koran does not follow a linear structure. The text seems to have no clear beginning, middle, nor end. Rather, it is sometimes criticised for its lack of continuity, and other times considered to be connected in a circular fashion, like a web or a net. The Old Testament of the Bible, on the other hand, is mostly chronological, beginning at the beginning of time. Jews even consider the Old Testament as a record of the history of their faith. Similarly, the Gospels, or the first four books of the New Testament in the Bible, are all accounts of the life and ministry of Jesus. Though they are not perfectly chronological, they do move in a linear direction. The Acts of the Apostles, another book in the New Testament, is a chronological record of the movement of the Christian ministry after Jesus' ascension into Heaven.
While both books contain both poetry and prose, the Koran is said to be written, in the original Arabic, with rhythm as well as rhyme. The Bible does not have this stylistic distinction.