Kant and Aristotle are both very concerned to develop a thick, discursive concept of rationality, which goes far beyond the merely logical to address many questions of what is right.
Nancy Sherman and others have substantially softened the traditional contrast between Kantian and Aristotelian ethics. Kant’s critique of eudaimonism (pursuit of happiness as an ethical criterion) was mainly aimed at the British utilitarians, who really did make subjective happiness into a criterion of sorts. It would be very wrong to think this applies to the Aristotelian notion. Sherman makes a strong case that in less familiar works dealing with moral anthropology, Kant recovers something like an Aristotelian notion of character. Kant’s extended development of the concept of judgment in the third Critique also recovers something like Aristotelian practical judgment or phronesis. (See also Freedom Through Deliberation?)
Aristotle and Kant have similarly thick notions of experience. In neither case is experience something immediate, as it was with the British empiricists. For Aristotle, it is as when we say someone is “experienced”. For Kant, it involves synthesis and extensive use of concepts, which themselves have complex derivation. Properly understood, Aristotelian “metaphysics” was concerned with higher-order interpretation of experience, and thus consistent with Kantian scruples. (See also Pure Reason, Metaphysics?)
Some of the argument of the paralogisms of pure reason is strongly reminiscent of things Aristotle said about the soul. Aristotle and Kant are equally opposed to Augustinian/Cartesian notions of reflexive constitutive immediacy. (See also God and the Soul; Modernity, Again.)
The main target of Kant’s attacks on dogmatism was the Wolffian school in Germany. He was not much concerned with the history of philosophy, and some of his language was overly sweeping. We should forgivingly take this into account in assessing the relation of the Critical philosophy to what I have called the epistemic modesty of Plato and Aristotle. (As Hegel recognized, Plato and Aristotle were not at all dogmatic. Plato doubted the deliverances of sense, and rejected opinion outright. Aristotle’s more optimistic, proto-pragmatist stance was elaborated in thoughtful response to that questioning. Neither of them was a simplistic realist. Moreover, the two of them were the original pioneers of rational inquiry in ethics.) Nonetheless, they did not anticipate the very substantial detail and development of Kant’s argument. The explicit concepts of the transcendental/empirical distinction and of unities of apperception are distinctly Kantian, as is a finer-grained analysis of processes of synthesis. (See also Copernican.)
Kant also more explicitly treated normativity as an outer frame around all other considerations. It is to him that we owe the notion of the primacy of practical reason. (See also Brandom and Kant; Hegelian Genealogy.) A stronger emphasis on ethical universality through the categorical imperative was another Kantian innovation.