Buddhism says: Nothing exists, but Advaita avers that it is not so. Advaita says there is Brahman.+

Sunyavadin Buddhists declared the nonexistence of Entity, a Void. This is just as much unwarranted finality, for it means one is viewing it from a particular standpoint as to declare its existence. Silence alone is called for. The absence or presence of the objective world and even existence and non-existence is always referred to witnessed only; it still leaves the formless witness untouched.

Existence means existence in the sense of the formless witness. When one reduces everything to consciousness, formless witness, Gnana, or even Mind, giving up all imaginations in truth it is unborn. One sees the waking experience come and go, but that is not the same as seeing him come and go, which one can never do.

First, one has become aware of the existence of a formless witness to distinguish it from the changeable objects in this world, but finally discards that position and rejects even the idea of Atmic existence after perfect understanding and assimilation of what is what. Then we may assert nothing about it. Not even existence or nonexistence i.e. silence alone is demanded by the truth.

“All is consciousness” meaning: “the whole universe is consciousness” because the universe is created out of consciousness. If consciousness is everything, how can there be anything other than consciousness? Hence silence is the nature of the Soul, the Self, which is present in the form of consciousness. 

The understanding comes after one becomes aware the Self is not the form, but the Self is the formless Soul or consciousness when all doubts have been cleared, all discussions ended, nothing more to assimilate.  There is no initiation for the realization of truth. 

Bhagvan 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. Buddha was not an atheist. He never denied the reality. There is nothing in his words or teaching to show that he considered the 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; 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 none 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 Buddha says clearly: Srmana Gautama was an atheist. It is the annihilation of the non-existent of 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-existent, which again is not mine? 

From these similar statements of Buddha, it is clear that he was not an atheist. All philosophers old and new arrives 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 devotee, only in an accurate way only from the standpoint of dvaithi.  After realization of oneness with God, there is no distinction between God and devote, and the word "devotion" has no meaning.   

Sage Gaudapada’s rational exposition of Advaita:~ Whatever is seen, whether external or internal, whether by the ordinary persons or yogis, is unreal.

If you are seeking truth you must set yourself free of all backgrounds, of all cultures, of all patterns of thinking and feeling. Even the idea of being a man or woman or even human should be discarded.

Advaitin disagrees with Buddhists who say, there is nothing - a nonentity. Advaitin 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, that exists forming the very substratum of all things.:~Santthosh Kumaar