Nietzsche most often addresses Buddhism as a rhetorical foil for Christianity, rather than analysing it directly.
Nietzsche exaggerates any aspects he approves in Buddhism as part of his rhetorical strategy. Buddhism is not moral, it is hygienic, prescribing a cure for the horror of the world rather than covering it up in dishonest grammar. In his highest praise of Buddhism, Nietzsche admits that it has dropped the slave morality—and the self-deception that accompanies it. Nietzsche describes Buddhism as clouded by morality. Perhaps specifically defining a thing as beyond good and evil keeps it trapped in the paradigm of defining the valuable by the valueless.
But Nietzsche only speaks favourably of Buddhism by comparison: when he mentions Buddhism apart from Christianity, it is all described as nihilism and desire for nothingness.
An Indian Nietzsche could easily have given Buddhism pride of place in the hierarchy of dangerous, life-denying institutions to discredit. Buddhism has perfected nihilism, but this is not a perfection to be desired.
But while