Schopenhauer is not an analytical philosopher by a long shot, he is placed firmly in the continental tradition, and so is Nietzsche. i'd say most analytical philosophers would get -analytically- nauseous when reading schopenhauer :D. Wittgenstein is usually considered the closest there is to a 'bridge' between continental and analytical tradition, tho definitively on the analytical side. said bridge being the nonsensical in Wittgensteins work. nuff said
i'd say the most fundamental difference between the two would be on morality. This is becomes perhaps most apparent in how either thinks about 'will'. Schopenhauer develops Kant's transcendental idealism further (in his own way) in the form of the 'will to live'. In short (and with a hacksaw for the sake of keeping it simple), at its basic level this would be the survival instinct. Schopenhauer then develops this further by adding moral awareness as a higher, reflective state of the will to live. Moral awareness is the development of the will-to-live so that it can escape the chaos and uncertainty of the animalistic 'law of the jungle' towards more tranquil, transcendent states of mind. the will-to-live reaffirms itself, transcending through morality, as mind. This transcendence is achieved, conversely, through a negation of the -immediate- will. going from the law of the jungle to moral law requires a more immediate affirmation of the will-to-live to be forgone.
for example: 'i want to eat you' when interrupted as a 'pure' -pre-reflective- act, becomes a (higher) awareness of said desire, if only for the moment it is negated. This is of course still a far cry from morality but it is this core that creates the room for the development of morality. the seed of culture lies in the negation of immediate desire. While this may be external, coincidental and of little consequence at first, the more it happens, the more it becomes part of the will, i.e. internalized in the will-to-live. Said negation is then further developed towards schopenhauers concepts of hope and despair, pessimism, asceticism etc.
Nietzsche does not disagree with all of this, but he sees the will-to-live as only an instance of a more general one, the will-to-power. In the will-to-power, the negation of will as a fundamental part of will is rejected in favor of its complete affirmation. thus, if the will is negated or negates itself, as schopenhauers will-to-live does, it only does so out of an ultimate desire for power. the development of tools, morality, etc. that serve the will is all the result of said will-to-power, and that is the way will affirms itself. Morality is not a higher, transcendent state of will but rather one particular emanation it. Morality is thus not an intrinsic part of will. will is beyond good and evil. evil is not a diminishing or lesser will, nor does good empower it. the will is simply there by means of its power; it affirms itself only by its power. life itself is will to power; self-preservation is only one of the indirect and most frequent results of that.
personally it seems to me it is possible to somewhat reconcile their views depending on interpretations of their fundamental concepts. They make different nuances and give more and/or less attention to certain areas as the other. though one could just as easily polarize i guess. To me it seems like nietzsche is reading schopenhauer in a particular way, and his interpretation is geared towards creating a dialectical opposition to clarify his own thought. Nietzsches foundation appears stronger as schopenhauers because the will is fundamentally undivided, yet for schopenhauer this fundamental division is a generative one, while in Nietzsches thought the will appears as somewhat too static perhaps. strangely enough he seems to rely on schopenhauers thought to get things moving. i dunno, i tend to keep thinking its 'two sides of the same coin, but then as different iterations of said coin' -different scratches etc.