The difference that atheism makes to the world is it requires an acceptance of this world as all there is. It requires a rejection of all beliefs that if we commit moral crimes we can be forgiven by accepting a Jewish zombie on our death bed or holding a belief in a circle of endless rebirth that will give us a second chance. It requires compassion for humanity in the here and now because there is no belief in an abstract entity that will provide compassion for us. (Notice that this does not occur in the current world because the compassion of gods have been passed on to the compassion of the state, and it did not happen in past worlds because child-raising was so brutal the compassion was crushed out of the culture before anyone reached adulthood.)
But most of all, it is important because it is a rejection of belief structures that require lying to and terrifying children for the sake of abstract entities. Only with this fundamental rejection of violence against children will we have a world with peace.
Tha'ts the last comment, by Paul C., on this page.