Basic Difference

Materialism and Advaita are poles apart.
Materialism says physical matter (including energy) is the fundamental substance in this world. Materialism says I am a temporary conglomerate of matter. Materialism says thoughts are the product of chemical and electrical changes happening in the physical brain, and Consciousness is just another thought.
Advaita says Consciousness is the fundamental substance in this world (prajnaanam brahma). I am pure Consciousness (chaitanyoham). Thus, I am the fundamental Reality (satyoham). I am the substance and substratum of this world (aham brahmaasmi).
Now, which is right? We have no capacity to judge because our judgment is only based on the inputs from the senses, their extending instruments and logic based on them. That will not help to judge here. All sensory inputs and scientific experiments are about the properties of objects. Here we are talking about two things: 1) the substance itself, 2) the subject itself. Both these are not accessible for study.
All the hair-splitting logic employed by the teachers of Advaita is to show how this hypothesis of Advaita based on the Vedas (sruti) does not contradict reason (yukti) and experience (anubhava). Also, the logic is to show how all the other hypotheses have self-contradictions, contradict experience and/or contradict the Vedas. In the course of thousands of years of this process, there are hundreds of hypotheses that are taken up and analyzed. These form the literature of the Advaita.
The beauty of the teaching of the Advaita teachers is to keep this stance as the Absolute Reality and still at a relative level give a working model of the triad of Jagat-Jiva-Ishwara and mapping it to the well known physical-mental-Conscious planes respectively. This provides a path for people to gradually understand the Absolute Reality using the concept of Ishwara as the prop in the relative level.