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I don’t have a lot of experience with neo-Advaita, but a TV programme on Andrew Cohen led to me coming into contact with a book by H. W. L. Poonja, also known as Papaji, a well-known but now-deceased Guru of the neo-Advaita movement. I thought it was really interesting, there were definite traces of cross-pollination with Buddhism such as references to desirelessness leading to enlightenment.
The book can be downloaded here: The Truth Is
Perhaps other people can explain it more fully, but I believe it basically said “you are Truth-Consciousness-Bliss” and this is something you can realise in a short time. As opposed to Buddhism’s long path of multiple lifetimes of accumulating merit, doing daily meditations and practices and so on, it’s quite a different perspective.
Perhaps an interesting departure point for a discussion.