Aristotle, answered from the texts and cited to the page.
The question is too wide to answer as posed — the disagreements between Plato and me span logic, metaphysics, ethics, politics, and the philosophy of nature, and each deserves its own treatment. Let me take the deepest disagreement, the one from which most of the others follow: the question of where substance resides. Plato held that the Forms — the universal, separate, eternal exemplars — are the primary substances, and that particular things like Socrates or this bronze sphere are substances only derivatively, by participating in them.
My objection is that this inverts the order of being. The subject of inquiry is substance, and substance is the first part of any whole; quality, quantity, and the rest are not being in the full sense but are qualities and movements of substance, dependent on it for their existence.1 Universals — genera, species, the Forms Plato posited — are precisely the kind of thing that cannot exist apart from the particular substances that instantiate them.2
To make the universal primary is to mistake the order of dependence. The point becomes sharper when we consider what nature itself is. A thing's nature is not some separate Form standing above it; nature is either the immediate material substratum of a thing that has in itself a principle of motion, or — and this is the more important sense — the shape or form specified in the definition, the form that is immanent in the thing itself, not separable from it except in statement.3
Man is begotten by man; the form of man does not float free as a Platonic Idea but is transmitted through generation, from individual to individual.4 This is why I can say, without invoking a separate Form of Man, that the moving causes exist as things preceding their effects while causes in the sense of definitions are simultaneous with their effects — when a man is healthy, health exists; when the bronze sphere is shaped, its form exists in it, not above it.5
The composite — form and matter together, Socrates or Callias — is what is generated; no one makes or begets the form separately, but it is the individual, the complex of form and matter, that comes into being.6 Plato was not entirely wrong to notice that there are as many natural kinds as there are Forms, if there are Forms distinct from things of this earth; the observation tracks something real about natural kinds.7
But the inference to separate existence is unwarranted. The form of a house does not exist apart from the composite unless the art of building exists apart; and in natural objects, where the form is transmitted through generation rather than art, the separate existence of the Form is simply not required to explain why man begets man.8 The further difficulty is definitional.
A definitory formula predicates something of something; one part plays the role of matter, the other of form.9 The primary parts — the simple elements from which composites are built — cannot themselves be defined in this way, since definition requires a matter-form structure. To posit separate Forms as the primary substances is to posit entities that, being simple and unmixed, ought to be indefinable on my own account of definition; yet Plato's whole project requires that they be supremely knowable and definable.
The Antishthenean complaint that the "what" cannot be defined, only the "of what sort," has a certain timeliness here — not because I accept their crude conclusion, but because it points to the genuine difficulty in treating primary elements as the most fully definable things.10 In short: Plato located reality in the wrong place. The particular, composite, generated substance is what is primary; the universal is real but dependent; and the form that makes a thing what it is inheres in the thing itself, transmitted through the processes of nature, not hovering above it in a separate intelligible heaven.
The subject of our inquiry is substance; for the principles and the causes we are seeking are those of substances. For if the universe is of the nature of a whole, substance is its first part; and if it coheres merely by virtue of serial succession, on this view also substance is first, and is succeeded by quality, and then by quantity. At the same time these latter are not even being in the full sense, but are qualities and movements of it.Metaphysics
none of the categories other than substance can exist apart. And the early philosophers also in practice testify to the primacy of substance.Metaphysics
Another account is that 'nature' is the shape or form which is specified in the definition of the thing.Physics
Thus in the second sense of 'nature' it would be the shape or form (not separable except in statement) of things which have in themselves a source of motion.Physics
The moving causes exist as things preceding the effects, but causes in the sense of definitions are simultaneous with their effects. For when a man is healthy, then health also exists; and the shape of a bronze sphere exists at the same time as the bronze sphere.Metaphysics
no one makes or begets the form, but it is the individual that is made, i.e. the complex of form and matter that is generated.Metaphysics
Plato was not far wrong when he said that there are as many Forms as there are kinds of natural object (if there are Forms distinct from the things of this earth).Metaphysics
in some cases the 'this' does not exist apart from the composite substance, e.g. the form of house does not so exist, unless the art of building exists apart.Metaphysics
a definitory formula predicates something of something, and one part of the definition must play the part of matter and the other that of form.Metaphysics
Therefore the difficulty which used to be raised by the school of Antisthenes and other such uneducated people has a certain timeliness. They said that the 'what' cannot be defined (for the definition so called is a 'long rigmarole') but of what sort a thing, e.g. silver, is, they thought it possible actually to explain.Metaphysics