According to a Wikipedia entry comparing Advaita Vedanta with Mahayana Buddhism,
Advaita Vedanta holds the premise, “Soul exists, and Soul (or self, Atman) is a self-evident truth.” Buddhism, in contrast, holds the premise, “Atman does not exist, and An-atman (or Anatta, non-self) is self-evident.”
This seems like a dubious “difference without a distinction” so long as one remains married to direct experience. To see this, we have to remember that all mystics are coming to a Reality that is prior to all language and therefore also prior to specific cultural, historical, and conceptual differences. Naturally, when they “report” on what they have directly discovered, they will avail themselves of the language–the analogies, the metaphors, and the concepts–that are ready to hand, sometimes using such culturally specific tropes in creative, innovative, and spellbindingly poetic ways.
Atman, recall, is the True Self. It is an answer to the question: “Who, really, am I?” And the answer, state spiritual adepts, sages, and saints, is that there is an unlimited, pure Awareness that, according to the dictates of dualistic language, will, alas, be put into the “subjective category,” the category of the “I.”
Now, when the Buddha suggests that anatta is true, he is saying that there is no such thing that “fits the bill” for being a personal, individuated, soul-like self. The Buddha’s, you see, is a deconstructive move: see through the illusion of a separate, allegedly self-standing self and then simply see who you really are.
This is so clear to one twentieth century Zen master, Shibayama, that, in The Gateless Barrier, he freely and without scruples calls ultimate reality Absolute Subjectivity. So much for that purported distinction!
Therefore, both are true: anatta points to the fact that no separate, personal self “holds together” the lived experience of any psycho-physical organism (human beings included) while Atman gives us an ultimate, positive answer to this pressing matter of ultimate concern. The Buddha demolishes while Advaita affirms. The via negativa and the via positiva here quite naturally join hands in universal fellowship and in pristine, reverent understanding.
A final word: we do well to trust the great mystical masters, not the scholarly debates that, so long as they are engaged in discourse alone, are starting off on the wrong foot. Chan, Zen, and Advaita Vedanta, in fact, all share a commitment to beginning, and ending, this existential inquiry into the nature of the ultimate by appealing first and above all to experience, not to scripture. The latter, yea a pointer, supports, but the former must bear the weight of the inquiry if this inquiry is to bear very beautiful fruit.