Was God dead as Nietzsche had said?
Had God died like Nietzsche said?
(The context is past-tense first-person narrative.)
What's the difference? And why?
Both of those are odd verb tenses for the context. I think it would have been better to phrase these:
Is God dead as Nietzsche said (he is)?
Did God die as Nietzsche said (he did)?
This makes the contrast between the two more obvious. "Is" asks about a condition, while "did" asks about an action.
The difference between these is subtle. "Is God dead?" could apply either to the actual, physical death of "God" or to a the death of the conceptual abstraction of a "God". Either way, the question asks about the resulting state, and not about the time, reason, or cause of death.
"Did God die?" can also refer to either the real or conceptual "God", but asks whether this action actually took place. Because it's more focused on the action, there is more attention to the details of when and why and who might have caused God to die, and not just whether the condition exists.