You may find logic in his version of if there’s no God everything is permitted. But that is only a small part of the whole. Most of hus books are disjointed series of aphorisms, Zarathustra included. It us shrewd and intermittently convincing. It is not convincing.
Anyway, the point is Hegel wax a logician,or at least laid out his own system of logic in detail. Nietzsche was something else altogether. Even in his books which contain extended arguments, for instance The Geneology of Morals, he doesn’t lay out any system. He just declares things.
Which I find meaningless in and of itself. The sophistication and scope of the construct doesn't necessarily enhance its persuasiveness. I would take the scattered insights of Nietzsche (but not his presuppositions), Pascal and Kierkegaard over the systematic breadth of Kant, Hegel and Descartes any day. But that's just me. Reasonable minds can differ which is what makes it all so much fun.