From the point of view of morality, believers tend to see a continuous progression and improvement, since we start with a jealous and petty God and end up with a gospel of agape (universal love) and altruism. Atheists agree with the claim of continuity, but morally they tend to lean in the opposite direction: the Bible has gone from really bad to absolutely awful: originally you would be punished for your actions (invariably exaggerated beyond all reasonable recognition, resulting in violent and torturous death); in the New Testament, however, you can even be found guilty of thoughtcrime, to borrow Orwell's coinage, and the punishment no longer ends in death: it follows you through an eternity of ceaseless and disproportionate torture and fiery hell.
But perhaps The Bible ought to be divided into three main parts instead of the traditional two: the Old Testament, the Gospels and Paul. Paul is continuous with the Old Testament, and carries its intolerance and vicious cruelty and totalitarianism to unfathomable new depths. Jesus, however, represents a major break and ideological departure from the legalistic obligations of the Old Testament and from Paul's self-righteousness on steroids.
As philosopher Don Cuppit argues in the following interview with Philosophy Bites, if we do to Jesus what Thomas Jefferson did with the Bible, namely take out all the supernatural attributions, what we eventually find is a philosopher (and no longer a fairy tale) who introduces the world to an unprecedented vision of radical humanism. The Jesus you find in the Bible is a prophet of death. Don Cuppit's Jesus represents a vision of life, fellow feeling and love.