Buddhism has no answer to certain questions like the existence of Atama.+

Buddha existed in India in a period 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. Buddha was charismatic, hypnotic. People were impressed by him. But the interpretation of Buddha was bound to be rational. 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. As I see Buddha, he was not primarily rational. The whole concept of nirvana is mystical. He 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 said, “Perfectly tame your own mind. This is the Buddha’s teachings." The Buddha did not say, “Perfectly tame others' minds.” We must purify our own minds. When you purify your mind you must begin with those who surround you every day, your family, friends, etc. Buddha says: Go alone, just remember two things. Don’t carry your mistakes — that means, don’t carry your past. There is no need even to repent about the past. Your religious people go on teaching you, “Repent!” because it is through repentance that they make you feel guilty, and when you are guilty you can be exploited. A real master always makes you feel good about yourself, not guilty; respectful towards yourself, not guilty. But the priests live on creating guilt in you. They would not like you to forget your mistakes; they want to remind you again and again. They have not even forgotten the sin that was committed by Adam and Eve; they go on reminding you about the original sin. You have not committed it, but you are born into the chain in which the first man and woman committed it and you are carrying the load of it. You have to feel guilty even for that, what to say about your own mistakes? The priests have lived in great power for the simple reason that they have reduced you into guilty sinners. - Osho

Sage  Sankara endeavored toward establishing the Vedic religion and overthrowing Buddhism. But even he was not able to avoid the influence of Buddhism. 

The influence of the revolutionary atmosphere of Buddhism reappeared in the Advaita of Sage Sankara. 

Sage Sankara's inability to revive the Vedic religion that flourished before the Buddhist revolution in its pure form is discernible.

Bhagavan 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.

Buddhism has no answer to certain questions like the existence of Atama (Soul). 

Dalai Lama said: ~ Buddhism need not be the best religion though it is more scientific and religion and inquisitive. But Buddhism has no answer to certain questions like the existence of Atama (Soul) and rebirth. Dali lama said that as an individual he believes in rebirth as he had come across a few cases of rebirth. Modern science, Dalai Lama hoped would unearth the mystery behind the rebirth. (In DH –dec-212009-Gulbarga).

Buddhi- sm has not proved the truth of Non-duality. There is no doubt 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 Advaita in speech but not to Advaita fully.

The distinction between Sage Sankara’s Advaitic wisdom and Vijnanavadin Buddhism are that the former is mentalism i.e. mind is the real, whereas the latter is idealism, i.e. ideas are real. We follow the former.

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

Bhagavan Buddha's teachings that all life is misery belong 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. Bhagavan 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   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.

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.

Bhagavan Buddha also holds that this world which changes from moment to moment is not real, it is only a reflection and a thing of which it is the reflection alone is real. Bhagavan Buddha was not an atheist. He never denied reality. There is nothing in his words or teaching to show that he considered truth to be non-existent like the horns of a hare. He could not have held the foolish view that something came out of nothing. It is true; that some of his disciples misunderstood and misinterpreted him. his idea was that the truth which cannot be designated by a name or described is words and of which one cannot even say whether it is existent or no extent, is like non-existent. The idea is quite in agreement with the view of the Upanishads. An object which cannot even be talked about, is, for all practical purposes, as good as non-extent. But it is not non-existent in the sense that the son of a barren woman is non-existent. This subtle idea, Buddha's contemporaries and even his disciple fail to catch. In one passage Bhagavan Buddha says clearly: Srmana Gautama was an atheist. It is the annihilation of non-existent truth that he teaches. So will people attribute to me atheism, which is not mine? So will they ascribe me to the theory of non-existence, which again is not mine?

From these similar statements of the Bhagavan Buddha, it is clear that he was not an atheist. All philosophers old and new arrivals at the same point. Orthodox 

Advaita (monism) is inevitable; the people of thoughtful temperament cannot find peace and quietude until they do so. Moksha (liberation) is in the realization of oneness with God. They speak of God Goddesses, devotion, and devotees, only in an inaccurate way only from the standpoint of dvaithi (dualists). After realizing oneness with God, there is no distinction between God and devote,e and the word "devotion" has no meaning.

Even in Buddhism: - Buddhist teaching has itself become a kind of interactive and Self-evolving process, much like its idea of pratityasamutpada. However, the end goal is still Nirvana, which is an experience ultimately beyond all concepts and language, even beyond the Buddhist teachings. In the end, even the attachment to the Dharma, the Buddhist teaching, must be dropped like all other attachments. The tradition compares the teaching to a raft upon which one crosses a swift river to get to the other side; once one is on the far shore; there is no longer any need to carry the raft. The far shore is Nirvana, and it is also said that when one arrives, one can see quite clearly that there was never any river at all. : ~Santthosh Kumaar