I notice in some reviews of the movie, people remark about how David displays a bevy of human feelings such as curiosity, love, happiness, etc. But the one feeling he is definitively lacking is fear. He demonstrates this during his relentless pursuit to unlock the Engineers' secrets within their base, without any consideration of the horrors that may arise from his discoveries. And it's embodied most splendidly when his severed head registers only a sort of disappointment and confusion upon being unexpectedly torn off by the enraged engineer.
Scott's Nexus 6's, by contrast, do have the capacity for this world-dread and sense of cosmic tragedy, and we can ascribe this to their human-like limited lifespan. Roy Batty's consciousness of his own mortality impels him to conjure the godhead and search for his place within the cosmogony, whereas David's immortality precludes him from doing so.