Both Mahayana and Theravada accept sankhara - that all things (except Nirvana) are conditioned and compounded. A tree doesn't exist by itself - it needs the sun and water and support from animals etc. Nothing lasts forever. Everything depends on something else - that's conditioned.
Advaita says Brahman is eternal, and everything else is an illusion. Hindus think Buddhism says the same thing as Advaita, that Brahman is same as Nirvana (as the only thing that is eternal) or Brahman is the same as shunyata (as the unity of everything), while illusion (maya) in Advaita is same as Madhyamaka's everything is empty of inherent substance or essence, and emptiness itself is empty of inherent substance of essence.
These sound superficially the same, but they are not the same.
This is supported by Banaras Hindu University Professor T. R. V. Murti's statement (quoted below) in this book chapter:
It has been the fashion to consider that the differences between the
Madhyamika śūnyatā and Brahman are rather superficial and even verbal,
and that the two systems of philosophy are almost identical. At least
Professor Radhakrishnan thinks so, and Stcherbatsky's and Dasgupta's
views are not very different. I hold a contrary view altogether: that
in spite of superficial similarities in form and terminology, the
differences between them are deep and pervasive.
When you compare Shankara's Advaita with Nagarjuna's Madhyamaka:
- Shankara said Brahman is eternal and absolute (see Vivekachudamani 225-231). Meanwhile, Nagarjuna said nothing is eternal and absolute.
- Shankara's Brahman (clay analogy - see Vivekachudamani 225-231) implies that it is the only thing that has a true inherent substance (what Nagarjuna called svabhāva). Meanwhile, Nagarjuna says nothing has inherent substance.
- Shankara's Brahman is the material cause (again, clay analogy) of the universe (see Vivekachudamani 225-231). Meanwhile, Nagarjuna's emptiness nor Nirvana is not a material cause for anything including itself.
- Shankara said that the universe depends on Brahman as its substratum (what Nagarjuna called para-bhāva) (see Vivekachudamani 235, 289). Meanwhile, Nagarjuna said there is no other inherent substance (para-bhāva) i.e. no substratum for anything else.
- Shankara's Brahman is the Ultimate Reality that is the Transcendental Absolute Reality. Meanwhile, Nagarjuna's Ultimate Reality is an "emptiness of emptiness" that is devoid of transcendental or absolute reality.
Advaita and Mahayana couldn't be more dissimilar.
Vivekachudamani 216 and Bhagavad Gita 2.20 talk about the individual soul (atman) being eternal. This is refuted by all Buddhist schools.
German indologist Professor Helmuth von Glasenapp wrote in his essay "Vedanta and Buddhism: A Comparative Study":
In the light of these researches, all attempts to give to the Atman a
place in the Buddhist doctrine, appear to be quite antiquated. We know
now that all Hinayana (sic) and Mahayana schools are based on the
anatma-dharma theory. ... Nirvana being a dharma, is likewise anatta,
just as the transitory, conditioned dharmas ... Nirvana is no
individual entity which could act independently. For it is the basic
idea of the entire system that all dharmas are devoid of Atman, and
without cogent reasons we cannot assume that the Buddha himself has
thought something different from that which since more than 2000
years, his followers have considered to be the quintessence of their
Nothing shows better the great distance that separates the Vedanta and
the teachings of the Buddha, than the fact that the two principal
concepts of Upanishadic wisdom, Atman and Brahman, do not appear
anywhere in the Buddhist texts, with the clear and distinct meaning of
a "primordial ground of the world, core of existence, ens realissimum
(true substance)," or similarly.
Madhyamaka says that everything is empty of inherent substance and even this emptiness is empty of inherent substance.
But what is this inherent substance?
After digging deep into this, I found that it is simply the essence or substance given to things by mental reification. It doesn't mean that a chair doesn't exist or that a chair is an illusion or the chair simply exists in my mind. It simply means that it doesn't exist the way my mind has mentally objectified and classified it. My mental idea of a chair has no inherent substance. This is perfectly supported by Theravada and the Pali suttas.
Without the thought of "I am the thinker", the mind would not be able to objectify and classify things relative to the self (observer). In this way, Theravada and Mahayana are completely united.
Advaita's eternal Brahman, which is the substratum of all reality and the material cause of reality, cannot be found in Buddhism.
Nagarjuna's greatest genius is proving that when you make use of the Buddha's teachings as metaphysics and philosophy, you turn it into mental reification that has no inherent substance. You talk about Nirvana, but that's only your mental idea of Nirvana, not how it really is.
Mahayana makes use of a lot of grandiose literary language. For e.g. the Eternal Buddha sounds a lot like Eternal Brahman.
But if you dig deeper into it, you find, that the Eternal Buddha in Mahayana refers to his Dharma Body.
The Dharma Body comes from the Vakkali Sutta (from the Theravada Pali Canon):
"For a long time, Lord, I have wanted to come and set eyes on the
Blessed One, but I had not the strength in this body to come and see
the Blessed One."
"Enough, Vakkali! What is there to see in this vile body? He who sees
Dhamma, Vakkali, sees me; he who sees me sees Dhamma. Truly seeing
Dhamma, one sees me; seeing me one sees Dhamma."
Vakkali wanted to see the Buddha's form, thinking he is special. But the Buddha used rhetorical speech to say that if you want to know what is special about the Buddha, understand the Dharma (the teachings of the Buddha). Mahayana took this to an extreme end and came out with Eternal Buddha.
Those who do not understand this, think Eternal Buddha is some God-person of some kind.
Similarly, Mahayana and Theravada are the same, if you look deeply enough, beyond the fancy language.
If you don't look deeply enough beyond the fancy language, Advaita and Mahayana appear to be the same, when it actual fact, they are only superficially the same.
Advaita is non-dual.
Non-dualism in Advaita is summarized by "Brahman (God) is real, the universe is an illusion. The jiva (individual soul) is Brahman itself and not different." (Brahmajnanavalimala 20)
In Advaita, Brahman (God) is the eternal, permanent and unchanging reality. But through ignorance, it appears as the changing universe and the individual soul. Remove ignorance, and Brahman is all that there is.
Both Mahayana and Theravada, are very much the same, and are non-dual too. But Buddhism is non-dual in a different way from Advaita.
In Buddhism, there is the duality of the self and the non-self. This is me, and this is my car and that is not my car. Everything perceived through the six senses (include the intellect and its sense objects - thoughts) is objectified and classified, relative to its relationship to the self.
As I wrote in another answer, a plate of cooked meat looks like delicious food to a meat eater, but it instead looks repulsive to a vegan. To a honey bee, it looks like dirt, because that is not its food. In this way, that plate of cooked meat is objectified and classified differently, relative to its relationship to the self.
The non-duality of Buddhism is that ultimately there is no self in all phenomena, and ultimately there is no inherent essence in all phenomena, as given to it by mental objectification and classification (relative to the self). Remove ignorance, and the duality of self and non-self falls apart.
In my opinion, Mahayana and Theravada are pretty much the same, just that Mahayana is more philosophical in its analysis and literary in its presentation, while Theravada is more pragmatic in its analysis and straightforward in its presentation.
Advaita on the other hand, is totally different, and is focused on the non-duality of God and non-God.