Sage Sankara's Advaita does not need the support of any scripture or revelation like the Vedas.+

Advaitic view~

Sage Sankara's system of Advaita does not need the support of any Scripture or Revelation like the Vedas. The Srutis may all disappear, yet will his school stand.  Since 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 tenet of Nirguna Brahman is true for Sage Sankara, not because it is taught by the Sruti, but because it is based on anubhava (intuitive experience) though it is also supported by the Sruti... The Advaitin knows that a legitimate doubt may have here to arise.  The Rishis may have truly spoken, but they may have been deluded themselves.  How are we certain that what the Rishis cognized is the Reality or Truth?  This can be proved according to the Advaita, only by the realization of truth beyond the form, time, and space.

And also:~

Again, in the absence of this realization, Nirguna Brahman as an object of thought is mere sound without sense. To one who has not seen a penguin, for instance, the word has no meaning ... Of what use, then, is such Sruti to him?  Similarly, common sense tells the Advaitin that the meaning of the Sruti and especially where there are conflicting interpretations is made out by means of reasoning based upon the authority of realization, which is final.

Thus, the reason comes into play between Sruti and realization corroborating the data of intuition with those of the revealed texts.

But reason also permits discrimination between the different possible experiences, for, in an a priori astonishing fashion:

Realization  ... can reveal not two, but twenty thousand conflicting experiences.  And the business of the wise is to sift the ultimate truth from out of all these ... The Advaitin rejects nothing.  All human experiences are his data.  He tests all by reason.

Only the Advaita can reply: it is the witness, the Seer. The Buddhists are in error in regards to the finite ego as illusory, and as having nothing more behind it: but they would have been perfectly correct in such outlook had they added the notion of the witness. How is it that Skandhas come together and compose the ego? Who sees them come and go? It is the witness, the Atman, and this lack Vedanta supplies in the seer and seen and reason Analysis. When they say that the mind comes and goes they are forgetting that there must be another part of the mind as consciousness that notices it and which tells them of this disappearance and appearance. All their misunderstandings arise from the fact that Buddha refused to discuss the ultimate questions. When Buddhism degenerates into Nihilism Advitin refutes it ( Manduka P.281).

The truth of a single reality within or underlying the illusory ego is all-important and without it Buddhism becomes fallacious.

Vedanta admits the transitoriness and evanescence of thoughts just like Buddhism, but not of the Mind which observes this transitoriness and knows it.

Manduka Upanishad:~  Buddhists borrowed from Upanishads because they were Indians. The Vedantins did not need to borrow from Buddhism therefore (P.396 v.99)

Bhagavan Buddha taught the illusoriness of ego but did not go further, probably because he thought the world could not understand the higher truth. Hence followers go with him to that point of his and then deny the Vedantic doctrine of one supreme reality when the Bhagavan Buddha himself neither denied nor advocated it. Anyway, the refutation of his followers is to ask them “What is it that is aware of the ego's illusoriness?" There must be something that tells you that. That something is the  Drik, and if you say this Drik itself may be illusory, coming and going, still there must be something non-transient i.e.permanent, to tell you this.

Bhagavan Buddha's teachings 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.

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 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.

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

Bhagavan Buddha as a constructive worker 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. Here  Sage Sankara was wiser and gave the religion; such as rituals and karma to the ignorant masses, as well as Advaitic wisdom to those who are capable to grasp the truth hidden by the 'I'. 

Bhagavan Buddha gave as the central feature of his doctrine the great law of Karma in order to reiterate its ethical meaning. He did more good in this to uplift the people than the ritualists.

Tibetan and Chinese Buddhists who 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, invisible body belongs to the realm of delusion or Self-deception. :~Santthosh Kumaar