Upanishads talk about transmigration of the Soul. Bhagvan Buddha talked about transmigration without a Soul.+

Dali Lama: ~ “If the scientific analysis were conclusively to demonstrate certain claims in Buddhism to be false, then we must accept the findings of science and abandon those claims.

H. H Dalai Lama was right in saying if the scientific analysis were conclusively to demonstrate certain claims in Buddhism to be false, then we must accept the findings of science and abandon those claims. it also proves his greatness and maturity how much importance he gives to the truth. 

Remember:~

It is quite true that Bhagavan Buddha constantly taught that man should seek release from transmigratory existence, but we must remember however that what the sage knows is known only to himself in its fullness and that he gives out to the public only so much as they could grasp and no more.

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

Bhagavan 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, 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.

Tibetan and Chinese Buddhists who say that many Buddhas are 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 Lord Shiva living on Mount Kailas in a spiritual body or Bhagavan Buddha in Nirmanakaya, invisible body belongs to the realm of delusion or Self-deception.

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. 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.

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 it come out of nothing.

Bhagavan Buddha: ~ “There are only two mistakes one can make along the road to truth: not going all the way... and not starting.

Dalai Lama said: ~ Buddhism need not be the best religion though it is most 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)

Bhagavan Buddha meant when he said the Self, did not exist, that the physical self alone did not exist.

 Atman:  real self. (Soul)

Jiva: physical self. (Ego)

Bhagavan Buddha said emptiness. Emptiness means the nature of the Soul, the fullness of the consciousness without the form, time, and space.

Bhagavan Buddha referred to the emptiness as "where thinking fails to attain", where words fail. All that you can say is there “No two". That is Advaita. 

Sunyavadins (Buddhists) say that Buddha taught void, and because Buddha went through Idealism, he is called an Idealist. Not so. Buddha cannot be pinned down. Buddha himself does not commit himself but says it is beyond words.

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

Even Buddhism is mixed up with regional culture and traditions of the local religion, wherever it existed. Thus to get the full essence from Buddhism is very difficult.

Dali Lama: ~ “If the scientific analysis were conclusively to demonstrate certain claims in Buddhism to be false, then we must accept the findings of science and abandon those claims.

Buddhism has not proved the truth of Nonduality. Buddha pointed out the unreality of the world, we agree. 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.

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.

Buddhist Sunyavada is incongruous 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. Therefore, the Sunya "non-entity" is meaningless without "entity". Both are there.

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.

When you say "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.

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

Sage Sankara opposed the Buddhists only, who misunderstood Bhagavan Buddha and became atheists. According to Sage Sankara meditation always means the critical analysis of the Self to get salvation from worldly tensions. Due to the eccentric ego of the then atheists, Sage Sankara did not go beyond this since the atheists will not accept God beyond themselves. This limitation is not due to limited knowledge of Sage Sankara but is due to the then-existing situation of the psychology of the surrounding society.

Even Bhagavan Buddha kept silent about God because the society dealt by Him consisted of Purvamimamsakas, who were strong atheists. 

Bhagavan Buddha told that everything including the Self is only relatively real (Sunya). This is correct because the Self is a part of the universe, which is relatively real to the absolute unimaginable God. Bhagavan Buddha stopped at this point because the atheists cannot realize the existence of the unimaginable God indicated through His silence. 

The point of Bhagavan Buddha is that if God is non-existent, the entire creation including ‘Self ‘is non-existent. Sage Sankara wanted to establish the existence of the Brahman. For this purpose, He made the Atman as the Brahman. He brought out the identity of Self with the consciousness and made the Atman the Brahman. Since one will not negate the existence of his Self, he will accept the existence of the Brahman, which is the Atman or Soul the innermost Self. 

Both Bhagavan Buddha and Sage Sankara kept silent about the absolute unimaginable God. The same philosophy was dealt with by them from different angles in different situations.

Sage Sankara disagrees with Buddhists who say, there is nothing - a nonentity. Sage  Sankara believes there is some reality, even though things are not what they appear to be. If one knows the truth, he will know what to do to find inspiration for action.  The seeker of truth‘s subject is to know what is it that is Real.

Buddhism says: all things are illusory and nothing exists.  However, Advaita avers that it is not so.  Advaita says that the universe, of course, is illusory, but there is Brahman (consciousness), that exists forming the very substratum of all things (illusion or universe). ~Santthosh Kumaar