Sage Sankara and Sage Goudapada, are not Buddhists, only a number of their ideas agree with those of Buddhism.+

Advaitic Sages disagree with Buddhists (Vijnanavadin) only on the Ultimate question, but they agree with their idealism fully.

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 non-duality, i.e. 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 an object only Buddhists are unaware of the subject.

ZEN may get a flash of peace but that is not the same as Advaitins who realizes that the world in which we exist is the Atman. Zen is mysticism.

Critics say Sage Sankara and Sage Goudapada borrowed their ideas from Buddhism. But in Manduka (page 281) these two declare Sage Sankara and Sage Goudapada, are not Buddhists, only a number of their ideas agree with those of Buddhism, whilst they point out their difference of view from Sunyavada Buddhists and Vijnanavadins. Thus, Sage Sankara and Sage Goudapada both agree and disagree with Buddhists.

Sunyavadins say there is nothing, neither matter nor mind: they are nihilists. How do they know the mind ceases to exist? Where is the proof? When you know everything is mind, both the changing forms and the underlying substances how can you posit its real change into nothingness? Mind, Brahman always remains really itself because of its nature. We see change every minute but by an inquiry into the nature of change and cause, we see that it is only when we imagine that there is cause and change.

The distinction between Sage Sankara's Advaita and Vijnanavadin Buddhism is 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 does not believe in the existence of the Athma whereas the Advatic Sages say Athma is the  Brahman or ultimate truth or God in truth. 

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 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, afterwards 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.

Sage Sankara gave religion; rituals and worship, etc.--to the ignorant populace and Advaitic wisdom to those who are capable of grasping the truth hidden by the Maya (world).

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