The distinguishing teaching about the Upanishads is that 1. God is not a person 2. The universe, as we perceive, is an illusion and its underlying reality is God 3. The individual (a person like you and me), is not just a collection of bones, muscles and tissue. Neither is the individual his/her mind. The true-nature of an individual is the indestructible Self. 4. The individual Self and God are one and the same.
There's no such teaching like this in the world. It blows my mind as I read and contemplate on the verses that talk about it. There are several saints who have realized this truth and their position on the issue of God, individual and world are identical to what the Upanishads teach.
IMHO A person who has put to test the teachings of the Upanishadic in his/her own life, and lives by its vision is a real teacher.