Psychiatry isn't a "rival" to faith healing; it is in itself a form of faith healing. Until psychiatric medicine can explain precisely how three pounds of bloody jello produces a properly functioning human mind, it has no hope of fixing one that isn't.
It is people's belief in the authority of the psycho-therapist and the drugs that they prescribe that effects the "cure" not the therapy or drugs themselves. Psychiatry is pseudo-scientific crap, albeit crap that sometimes makes people feel better. In that regard it is no different than homeopathy, acupuncture or the laying on of hands.