One of the major aspects of Milton's account of the Book of Genesis which is different is the way that Milton focuses on the freedom that God gives to man. God creates them "free to fall," and this is something that is shown to be essential to their very nature. They must be able to defy God if their relationship with him is to mean anything at all. This is why in Book III God says that he "formed them free, and free they must remain." Milton therefore majors much more heavily on the whole aspect of free will.
This is because Milton believed that choosing to be obedient was to be seen as a sign of mankind's adoration to God. Obedience has to be a choice for it to mean anything. If it were a pre-programmed, robotic response, it would be meaningless. A key theme of Milton's rewriting of Genesis is therefore this aspect of free will and how God created Adam and Eve to possess it, even though this opens up the possibility of their disobedience.
Apart from this, there are many other differences such as the role of Satan and the background we are given about him. Milton parallels the Fall of Man with the fall of Satan and his minions, and the two provide a very interesting counterpoint.