There is the advantage that mystic, unlike psion* or psionicist, is a real word. Psionic is real ("pertaining to the telepathic, psychic, or paranormal") but neither psionicist nor psion are; they are adding a suffix to change the part of speech (cist) or shorting the word. Really, the term should be "psychic" or "medium" if they were keeping the psuedoscience nomenclature.
Mystic, while plain, does invoke a bit of otherworldly, meditative, and "secrets of the universe" feel. The other two terms invoke "uses psionics".
* Psion is on dictionary.com, but as the proper noun of a UK tech company. Not what you'd want for your fantasy psionic character.