Advaita is tricky. It has different teachings for different levels of teaching. Most of what Buddhists criticize are the first level, provisional teachings: finding the witness, believing in an independent self, etc. At higher levels, these concepts are dissolved.
David Loy has persuasively argued for the similar goals of the teaching in the article I posted much earlier.
Nirguna Brahman is beyond all concepts. Anything we say about Nirguna Brahman is wrong.
The best description of awareness I've found in Buddhist teaching is that of Ajahn Sumedho. Unlike many, Ajahn Sumedho does not deny it. Nor does he posit a self, as he is often accused of doing. I've quoted him at length below.
[url]http://www.dhammatalks.net/Books3/Ajahn ... n_Time.htm
Q: This word 'citta' is used in the suttas for the subjective consciousness. If there's a citta from which the asavas (biases) are removed and a citta which is liberated, how does this fit in with the idea of self or no-self? How does one avoid self-view in thinking about the citta? If there's no self, who is it that's aware and what is it that becomes enlightened?
A: This is where Buddhism excels. It totally frustrates that desire. The Buddha wouldn't give an inch on that, because that's the non-dualism of the Buddha's teaching. It's psychologically uninspiring. You're left with just letting go of things rather than holding on to the feeling of a God or Oneness or the Soul or the Subject with capital S, or the Overself, or the Atman or Brahman or whatever - because those are all perceptions and the Buddha was pointing to the grasping of perception. The "I am" is a perception - isn't it? - and "God" is a perception. They're conventionally valid for communication and so forth, but as a practice, if you don't let go of perception then you tend to still have the illusion - an illusoriness coming from a belief in the perception of the overself, or God or the Oneness or Buddha Nature, or the divine substance or the divine essence, or something like that.
Like with monism - monistic thinking is very inspiring. "We're all one. We are one - that's our true nature - the one mind." And you can talk of the universal mind and the wholeness and the oneness of everything. That's very uplifting, that's the inspiration. But non-dualism doesn't inspire. It's deliberately psychologically non-inspiring because you're letting go of the desire for inspiration, of that desire and need and clutching at inspiring concepts. This doesn't mean that those concepts are wrong or that monistic thinking is wrong; but the Buddha very much reflected the attachment to it. So, you're not an annihilationist saying there's nobody, nothing, no subject, but by non-dualism, you just let go of things till there's only the way things are.
Then who is it that knows? People say: "Then what is it that knows? Who is it that knows the way things are, who is it that's aware? What is it that's aware?" You want me to tell you? I mean you're aware aren't you? Why do you have to have a name for it? Do you have to have a perception? Why can't there just be awareness? Why do you have to call it mine, or the eternal essence, or whatever? Why do you have to name it? Why not just be that, be aware. Then you see the desire, the doubt, wanting to label it, add to it. It's avijja paccaya sankhara (creating conditions out of ignorance). The process goes on of wanting to complicate it by giving it a name, calling it something.
Just like the question "Can you see your own eyes?" Nobody can see their own eyes. I can see your eyes but I can't see my eyes. I'm sitting right here, I've got two eyes and I can't see them. But you can see my eyes. But there's no need for me to see my eyes because 1 can see! It's ridiculous, isn't it? If I started saying "Why can't I see my own eyes?" you'd think "Ajahn Sumedho's really weird, isn't he!" Looking in a mirror you can see a reflection, but that's not your eyes, it's a reflection of your eyes. There's no way that I've been able to look and see my own eyes, but then it's not necessary to see your own eyes. It's not necessary to know who it is that knows-because there's knowing. And then you start creating views about who is it that knows, then you start the avijja paccaya sankhara and on through the whole thing again to despair and anguish.