Yes the first five books are commonly known as 'The Torah', but if I am correct within Jewish communities it is referred to as 'The Talmud'. The literal translation of 'torah' is 'law' and these are known as the books of law which govern everyday life of a Jewish believer.
I have never read the Koran although I am aware of an English translation of the Koran in the iTunes bookstore being available.
So technically, I have read the Bible and the Torah.
As for the differences, I don't think we can discuss them openly here in case we get into a religious debate but it can be discussed privately off the forum.
The Torah is very straight forward accounts of historical facts according to the Jews and it tells of Jewish family lineage as well as spelling out the statutes, regulations, and laws that every Jew must follow, from dietary restrictions to their private lives and keeping themselves ritually clean. It also gives very specific details of the old temple that was built by Solomon, down to how many utensils there should be and what type of metal they are to be cast from. It's very specific and very detailed with a lot of 'begats'
The new testament is more contemporary and it gives instructions on every day Christian living, from blessing ones food before eating, down to when a married couple should get it on.
Each book has its own writing style, some are narrative form, some are poetic, and some are in letter form.