Bhagavan Buddha talked about transmigration without a Soul. It is more mystical.+

Buddha was charismatic and hypnotic. Buddhism did not graduate its teaching to suit people of varying grades; hence its failure to affect society in Asia. People were impressed by him. But the interpretation of Buddha was bound to be rational. 

Buddha existed in India centuries back when the whole country was going through a crisis of everything irrational: the Vedas, the Upanishads, the whole mysticism. The movement against all this was very great, particularly in Bihar where Buddha was.

If Buddha had lived at another time in history, in a part of the world that was not against mysticism, he would have been seen as a great mystic, not as an intellectual. The face that is known belongs to the history of a particular time. Buddha was not primarily rational. The whole concept of nirvana is mystical.

Buddha was even more mystical than the Upanishads, because the Upanishads, however, mystical they look, have their own rationality. They talk about the transmigration of the Soul. Buddha talked about transmigration without a Soul. It is more mystical.

Buddha said:~ The Upanishads talk about liberation, but you will be there. Otherwise, the whole thing becomes nonsense. If I cannot be in that ultimate state of existence, then the whole effort is useless and illogical. Buddha said the effort is to be done – and you will not be there. It will just be nothingness. The concept is more mystical. ~ (OSHO)

Buddha was a constructive worker who committed an error in failing to give the masses a religion, something tangible they could grasp something materialistic, if symbolic that their limited intellect could take hold of, in addition to his ethics and philosophy.

Buddha kept silent, refusing to answer questions on the ultimate. Therefore, he was the wisest man in refusing to commit himself.

Nonduality does not need the support of any Scripture or Revelation like the Veda. For it is based, not upon the varying theological fancies, which are as numerous as the sands of the sea, but upon reason, the common heritage of all mankind, irrespective of color or creed or clime.

The Seeker of truth has to know that something is inadequate in Buddhist or orthodox Advaitic teachings to reach the nondual destination because of the add-ons and adulteration. Thus, it becomes difficult to reach the destination directed by the Buddha.

Buddha gave up yoga after practicing it for six years. He saw it could not yield truth.

Buddha gave up his austerities of yoga as impossible and useless. Thus Buddha got enlightenment only after he gave up Yoga. Unless one exercises his --reason--there is no chance of getting the truth. - (Page.70/71 "Buddhism in Translation” by Warren)

Buddhism has not proved the truth of Nonduality.  Buddha pointed out the unreality of the world. He told people they were foolish to cling to it. But he stopped there. He came nearest to Vedanta in speech but not to Vedanta fully.

Buddha's teaching that all life is misery belongs to the relative standpoint only. For you cannot form any idea of misery without contrasting it with its opposite, happiness. The two will always go together. Buddha taught the goal of cessation of misery, i.e. peace, but took care not to discuss the ultimate standpoint for then he would have had to go above the heads of the people and tell them that misery itself’ was only an idea, that peace even was an idea (for it contrasted with peacelessness). That the doctrine he gave out was a limited one, is evident because he inculcated compassion. Why should a Buddhist sage practice pity? There is no reason for it. Advaita is the next step higher than Buddhism because it gives the missing reason, viz. unity, non-difference from others, and because it explains that it used the concept of removing the sufferings of others, of lifting them up to happiness, only as we use one thorn to pick out another, afterward throw both away. Similarly, Advaita discards both concepts of misery and happiness in the ultimate standpoint of non-duality, which is indescribable.

Buddha gave as the central feature of his doctrine the great law of Karma to reiterate its ethical meaning. He did more good in this to uplift the people than the ritualists. Buddha: ~ Do not believe in anything merely on the authority of your teachers and elders. It is better to conquer yourself than to win a thousand battles. Then the victory is yours. It cannot be taken from you, not by angels or by demons, heaven or hell.

Buddhists say that a thing exists only for a moment, and if that thing has still got some of the substance from which it was produced how then can they deny that its cause is continuing in the effect; hence its existence is more than a moment. Vedanta is concerned with whether it is one and the same thing which has come into being or has come out of nothing.

Even the Sunyavada ultimate of the "void" is really a breath, and therefore an imagination and not truth.

Buddhism did not graduate its teaching to suit people of varying grades; hence its failure to affect society in Asia.

Buddhists say that a thing exists only for a moment, and if that thing has still got some of the substance from which it was produced how then can they deny that its cause is continuing in the effect; hence its existence is more than a moment. Vedanta is concerned with whether it is one and the same thing which has come into being or has come out of nothing.

Even the Sunyavada ultimate of the "void" is really a breath, and therefore, imagination and not the truth.

Buddhism did not take people to the ultimate truth but showed them the worthlessness of desire-filled worldly life. It is good as far as it went, but this led to an overemphasis on outward renunciation, so here Sage Sankara differs from Buddha. Buddha did not show that Brahman (consciousness) is also in the world.

Tibetan Buddhists say that there are many Buddhas living in spirit bodies and helping our earth from the spiritual world are still in the sphere of religious illusion, not the ultimate truth. Their statements are wrong. Every sage realizes that the only way to help mankind is to come down amongst them, for which he must necessarily take on flesh-body. When people are suffering how can he relieve their suffering unless he appears amongst them? When people are suffering how can he feed them from an unseen world whether their struggle is for material bread or for spiritual truth? No! He must be here actually in the flesh. It is impossible to help them in any other way and all talk of Shiva living on Mount Kailas in the spiritual body or Buddha in Nirmanakaya, the invisible body belongs to the realm of delusion or ‘Self’-deception.

Sunyavada Buddhism is no intelligible meaning because every thought has its opposite every word is tied to its coordinate for all thought and speech can only operate under such dualism. Hence, taking the most fundamental word, existence is implied opposite non-existence is also there, and vice versa. So the Sunya "non-entity" is meaningless without "entity". Both are there.

When one says "Nothing is" what is the meaning of "is"? "Sunya" is something that exists: you cannot prove that consciousness does not exist. Has the Void a meaning? If so then it is only your imagination.

Even when you say "I am not" you are thinking. Hence, every thought means positing some existence. To exist is to be thought of hence our criticism of Sunyavada which says there is nothing. In saying "There is nothing,  they are unconsciously positing something. The thought of nothing is existence itself. Hence, only by refraining from thought can they state their case. The thought itself is an object. The negation of existence is a thought. The presence of an object means duality. Hence, this proves that the Sunyavadins never understood the non-duality that is Brahman.

Buddhism agrees in thinking that the ego sees itself; they do not admit there is anything that sees the ego: they say there is no proof that any witness exists. When thoughts are there, thoughts become conscious of themselves.  Skandhas which appear and disappear are the object only Buddhists are unaware of the subject.

Buddhist Idealism: speaks only of ideas. What about the knower of these ideas? Buddhist Nihilism does not ask "What is meant by Nihilism? It is a thought. There must be a thinker of this thought.

Sage Sankara disagree with Buddhists (Vijnanavadin) only on the ultimate question, but they agree with their idealism fully.:~Santthosh Kumaar