As I say in my comment to your question I have never heard as these being ‘the’ two schools of Advaita. None of my teachers have ever mentioned these as schools. I did however find one reference to the two schools and their differences so I will reproduce it contents below. I don’t pretend to be a great scholar of the Advaita or to have read every book or commentator out there. Most commentators and modern teachers either comment on Sankara and his teachings directly or use the commentaries of their modern lineage.
Having said that, let me first reference the commentary I found on the two schools and then try to formulate how I think most modern Advaitists would answer your question.
The Introduction to Swami Swahananda’s translation of Sri Vidyaranya Swami’s Pancadasi (Vidyaranya was the Sankaracharya of the Sringeri Math from 1377-1386) is written by T. M. P. Mahadevan, Director, Centre of Advanced Study in Philosophy, University of Madras. In it he says:
In what manner is the appearance of the jiva to be understood? In regard to this question, there is some difference of opinion between the two main post-Sankara Advaita Schools—the Vivarana and the Bhamati. According to the Vivarana view, the jiva is a reflection of Brahman in Nescience, and Brahman as the prototype reflected is Isvara. This view is known as pratibimba-vada. The Bhamati view, which is called avaccheda-vada, is that the jiva is Brahman as defined or delimited by nescience [Avidya or Maya]. The analogy for the former view is the reflection of the face in the mirror; that for the latter view is the delimitation of ether by pot, etc. Sri Vidyaranya who follows mainly the Vivarana tradition, teaches a modified form of the reflection-theory which is referred to as abhasa-vada. While the Vivarana view regards the reflection as real and as identical with the prototype, the theory sponsored in the Pancadasi holds that the reflection (abhasa) is mere appearance, an illusory manifestation. The apposition between the jiva and Brahman, according to this view, is through sublation (badha), and not through identification (aikya).
…What is the immediate instrument of release? Is it sravana of the mahavakya ‘That thou art’? Or, is it continued meditation (also called prasamkhyana)? On this question, the two post-Sankara Advaita schools, already referred to, are divided. According to the Bhamati view, verbal testimony (sabda) of which the mahavakyas form part, can yield only mediate knowledge, and not immediate or direct knowledge. If the mediate knowledge gained from verbal testimony is to be transformed into immediate experience, there should be continued meditation till this is achieved; and this is possible because the mind which is the instrument in meditation is a sense organ (indriya). The Vivarana view maintains that the mind is not a sense organ, as it is an auxiliary to all pramanas and that verbal testimony can yield immediate knowledge…Thus verbal testimony can convey immediate knowledge if the object is immediate. There is no object more immediate than the Self. Hence, the mahavakya ‘That thou art’ imparts to the competent hearer the direct experience of the non-dual Self. Giving a citation from the Vakyavrttii Sri Vidyaranya says, “The major texts are for the sake of imparting direct knowledge of Brahman. In regard to this there is no room for doubt” (Pancadasi VII, 70)…Meditation, however, is not without its great use. In chapter IX, Dhyana-dipa, Sri Vidyaranya compares it to samvadi-bhrama, delusion which culminates in a fruitful result…Thus, for those who are not qualified for gaining true knowledge through enquiry, Sri Vidyaranya recommends the Yoga of meditation (dhyana).
In the first paragraph you will note that Professor Mahadevan calls the teaching of Vidyaranya Swami a modified Vivarana called abhasha-vada. From my own experience, my opinion is that this is the view held and taught by most modern Advaitists.
Sankara says in his Vivekachudamani:
Avidya. (Nescience) or Maya, called also the Undifferentiated, is the power of the Lord. She is without beginning, is made up of the three Gunas and is superior to the effects (as their cause). She is to be inferred by one of clear intellect only from the effects She produces. It is She who brings forth this whole universe.
She is neither existent nor non-existent nor partaking of both characters; neither same nor different nor both; neither composed of parts nor an indivisible whole nor both; She is most wonderful and cannot be described in words.
According to Sankara, Brahman has nothing to do with Avidya. The example of the snake and the rope is given (Vivekachudamani 246). Does a rope have anything to do with the fact that an observer sees a snake instead of a rope? No – the illusion of the snake lies entirely with the observer. The illusion is only on the part of the observer. Your statement that “Brahman is the locus of Avidya” is true – insofar that without the existence of the rope, there could be no illusion of the snake projected onto it. But to infer that Brahman is the ‘cause’ of the illusion or possesses Avidya is not true.
Sankara says further (Vivekachudamani):
Man’s transmigration is due to the evil of superimposition, and the bondage of superimposition is created by the mind alone. It is this that causes the misery of birth, etc., for the man of non-discrimination who is tainted by Rajas and Tamas.
Hence sages who have fathomed its secret have designated the mind as Avidya or Ignorance, by which alone the universe is moved to and fro, like masses of clouds by the wind.
And also:
241-242. If thus the Sruti, in the dictum “Thou art That” (Tat-Tvam-Asi), repeatedly establishes the absolute identity of Brahman (or Isvara) and Jiva, denoted by the terms That (Tat) and Thou (Tvam) respectively, divesting these terms of their relative associations,--then it is the identity of their implied, not literal, meanings which is sought to be inculcated, for they are of contradictory attributes to each other—like the sun and a glow-worm, the king and a servant, the ocean and a well, or Mount Meru and an atom.
This contradiction between them is created by superimposition, and is not something real. This superimposition, in the case of Isvara (the Lord), is Maya, or Nescience, which is the cause of Mahat and the rest,--and in the case of the Jiva (the individual soul), listen,--the five sheaths, which are the effects of Maya, stand for it.
These two are the superimpositions of the Isvara and the Jiva respectively, and when these are perfectly eliminated there is neither Isvara nor Jiva. A kingdom is the symbol of a king, and a shield of the soldier, and when these are taken away there is neither king nor soldier.
- Whatever a deluded man perceives through mistake, is Brahman and Brahman alone: The silver is nothing but the mother-of-pearl. It is Brahman which is always considered as this universe, whereas that which is superimposed on the Brahman, viz., the universe, is merely a name.
Swami Vivekananda says:
Maya is not illusion as it is properly interpreted. Maya is real, yet it is not real. It is real in that the Real is behind it and gives it its appearance of reality. That which is real in Maya is the Reality in and through Maya. Yet the Reality is never seen; and hence that which is seen is unreal, and it has no real independent existence of itself, but is dependent upon the Real for its existence.
Maya then is a paradox—real, yet not real, an illusion, yet not an illusion.
He who knows the Real sees in Maya not illusion, but reality. He who knows not the Real sees in Maya illusion and thinks it real.
Maya is called anirvachanya – inexpressible. Hence its description by Sankara as vivarta-vada, an ‘apparent manifestation’ It is neither real nor is it unreal. Brahman is not affected by it nor is it a part of Brahman.
