Even when religion claims to ground morality it affirms its transcendence over morality, hence its essential difference and autonomy from the rule of morality.
In monotheism in particular, there is a "good" and a "bad" because God decides so, not the other way around. This places God above any moral code by definition.
Believers unwittingly reverse the religious order when they affirm that their God is right, or good, unless they mean it in a purely tautological way (which is rarely the case). This is actually a denial of transcendence, as if God could be measured by a superior moral principle.
But the very fact that this happens (all the time) reveals the constant tendency of morality to become absolute. Even God cannot escape to be judged by his ownrules in the long run, although he was meant to be above them in principle.
A godless world is definitely a more moral one (regardless of the actual contents of morality), in a both positive and scary sort of way. It means that there is no commonly acknowledged exception to morality, and that we have nobody but ourselves to appeal to against the essential totalitarianism of morality.
