Sri Aurobindo
Buddhism seemed to reject all spiritual continuity with the Vedic religion. But this was after all less in reality than in appearance. The Buddhist ideal of Nirvana was no more than a sharply negative and exclusive statement of the highest Vedantic spiritual experience. The ethical system of the eightfold path taken as the way to release was an austere sublimation of the Vedic notion of the Right, Truth and Law followed as the way to immortality, ṛtasya panthā. The strongest note of Mahayana Buddhism, its stress on universal compassion and fellow-feeling was an ethical application of the spiritual unity which is the essential idea of Vedanta. The most characteristic tenets of the new discipline, Nirvana and Karma, could have been supported from the utterances of the Brahmanas and Upanishads. Buddhism could easily have claimed for itself a Vedic origin and the claim would have been no less valid than the Vedic ascription of the Sankhya philosophy and discipline with which it had some points of intimate alliance.
But what hurt Buddhism and determined in the end its rejection, was not its denial of a Vedic origin or authority, but the exclusive trenchancy of its intellectual, ethical and spiritual positions. A result of an intense stress of the union of logical reason with the spiritualised mind,—for it was by an intense spiritual seeking supported on a clear and hard rational thinking that it was born as a separate religion,—its trenchant affirmations and still more exclusive negations could not be made sufficiently compatible with the native flexibility, many-sided susceptibility and rich synthetic turn of the Indian religious consciousness; it was a high creed but not plastic enough to hold the heart of the people. Indian religion absorbed all that it could of Buddhism, but rejected its exclusive positions and preserved the full line of its own continuity, casting back to the ancient Vedanta.
THE INCARNATE WORD: VOLUME 14: https://incarnateword.in/sabcl/14/religion-and-spirituality-ii
Ananda Coomaraswamy on Buddhism
The more superficially one studies Buddhism, the more it seems to differ from the Brahmanism in which it originated; the more profound out study, the more difficult it becomes to distinguish Buddhism from Brahmanism, or to say in what respects, if any, Buddhism is really unorthodox. The outstanding distinction lies in the fact that Buddhist doctrine is propounded by an apparently historical founder, understood to have lived and taught in the sixth century B.C. Beyond this there are only broad distinctions of emphasis.
…It is taken almost for granted that one must have abandoned the world if the Way is to be followed and the doctrine understood. The teaching is addressed either to Brahmans who are forthwith converted, or to the congregation of monastic Wanderers (parivrajaka) who have already entered on the Path; others of whom are already perfected Arhats, and become in their turn the teachers of other disciples. There is an ethical teaching for laymen also, with injunctions and prohibitions as to what one should or should not do, but nothing that can be described as a “social reform”‘ or as a protest against the caste system. The repeated distinction of the “true Brahman” from the mere Brahman by birth is one that had already been drawn again and again in the Brahmanical books.
… It is in fact surprising that such a body of doctrine as the Buddhist, with its profoundly other worldly and even anti-social emphasis, and in the Buddha’s own words “hard to be understood by you who are of different views, another tolerance, other tastes, other allegiance and other training”, can have become even as “popular” as it is in the modem Western environment. We should have supposed that modern minds would have found in Brahmanism, with its acceptance of life as a whole, a more congenial philosophy. We can only suppose that Buddhism has been so much admired mainly for what it is not (italics mine). A well known modern writer on the subject has remarked that “Buddhism in its purity ignored the existence of a God; it denied the existence of a soul; it was not so much a religion as a code of ethics”. We can understand the appeal of this on the one hand to the rationalist and on the other to the sentimentalist. Unfortunately for these, all three statements are untrue, at least in the sense in which they are meant. It is with another Buddhism than this that we are in sympathy and are able to agree; and that is the Buddhism of the texts as they stand.
…We believe that enough has now been said to show beyond any possible doubt that the “Buddha” and “Great Person”, “Arhat”, “Brahma-become” and “God of Gods” of the Pali texts is himself the Spirit (atman) and Inner Man of all beings, and that he is “That One” who makes himself manifold and in whom all beings again “become one”; that the Buddha is Brahma, Prajapati, the Light of lights, Fire or Sun, or by whatever other name the older books refer to the First Principle; and to show that insofar as the Buddah’s “life” and deeds are described, it is the doings of Brahma as Agni and Indra that are retold. Agni and Indra are the Priest and King in divinis, and it is with these two possibilities that the Buddha is born, and these two possibilities that are realised, for although his kingdom is in one sense not of this world, it is equally certain that he as Cakravartin is both priest and king in the same sense that Christ is “both priest and king”.
… We are forced by the the logic of the scriptures themselves to say that Agnendrau, Buddha, Krishna, Moses and Christ are names of one and the same “descent” whose birth is eternal; to recognize that all scripture without exception requires of us in positive terms to know our Self and by the same token to know what-is-not-our-Self but mistakenly called a “self”: and that the Way to become what-we-are demands an excision from our consciousness-of-being, every false identification of our being with what-we-are-not, but think we are when we say “I think” or “I do”. To have “come clean” (suddha) is to have distinguished our Self from all its psycho-physical, bodily and mental accidents; to have identified our Self with any of these is the worst possible sort of pathetic fallacy and the whole cause of “our” sufferings and mortality, from which no one who still is anyone can be liberated.
… It is altogether contrary to Buddhist, as it is to Vedantic doctrine to think of “ourselves” as wanderers in the fatally determined storm of the world’s flow (samsara). “Our immortal Self” is anything but a “surviving personality”. It is not this man So-and-so that goes home and is lost to view, but the prodigal Self that recollects itself; and that having been many is now again one, and inscrutable, Deus absconditus. “No man hath ascended up to heaven, but he that came down from heaven”, and therefore “If any man would follow me, let him deny himself”. “The kingdom of God is for none but “the thoroughly dead”. The realisation of Nirvana is the “Flight of the Alone to the Alone”.
(From Hinduism and Buddhism– a short but phenomenal book explaining the essence of Vedanta and Buddhism and shows their “differences” as scholarly misunderstandings of both)