Both individuals are promoting a spirituality and or a form of mysticism based primarily on Buddhism and/or Advaita Vedanta.
Not really. While Harris identifies certain dharmic traditions as having picked up insight as a result of their contemplative traditions of yoga/mediation, he rejects the leap from the experience of these altered states of consciousness that are made by some New Age advocates, including Deepak Chopra. You can just
read this from the man himself:
Authors who attempt to build a bridge between science and spirituality tend to make one of two mistakes: Scientists generally start with an impoverished view of spiritual experience, assuming that it must be a grandiose way of describing ordinary states of mind—parental love, artistic inspiration, awe at the beauty of the night sky. In this vein, one finds Einstein’s amazement at the intelligibility of Nature’s laws described as though it were a kind of mystical insight.
New Age thinkers usually enter the ditch on the other side of the road: They idealize altered states of consciousness and draw specious connections between subjective experience and the spookier theories at the frontiers of physics. Here we are told that the Buddha and other contemplatives anticipated modern cosmology or quantum mechanics and that by transcending the sense of self, a person can realize his identity with the One Mind that gave birth to the cosmos.
Chopra certainly falls in the latter category. He promotes
Ayurvedic medicine, and wisely perceives skeptics as his natural enemy,
writing in 2010 that "No skeptic, to my knowledge, ever made a major scientific discovery or advanced the welfare of others." He also wrote this:
So whenever I find myself labeled the emperor of woo-woo, I pull out the poison dart and offer thanks that wrong thinking has gotten us so far. Thirty years ago no right-thinking physician accepted the mind-body connection as a valid, powerful mode of treatment. Today, no right-thinking physician (or very few) would trace physical illness to sickness of the soul, or accept that the body is a creation of consciousness, or tell a patient to change the expression of his genes. But soon these forms of wrong thinking will lose their stigma, despite the best efforts of those professional stigmatizers, the skeptics.
I can guarantee you that Harris, while open to empirical research into certain claims (including, for example, the survival of consciousness after death), is not claiming that physical illness represents soul sickness, or
that patients can change the expressions of their genes. This endorsement of "self-help epigenetics" is astonishing since it finds such wide reception, and is sadly co-signed by the equally dubious Rudy Tanzi, a Harvard PhD with the same habit of making bold, ungrounded claims about "spiritual" applications of science, or alternatively scientific endorsements of spiritual beliefs.
Jerry Coyne demolishes their nonsense pretty quickly and clearly.
The two men are light years apart.