Psychological therapy could not possibly work the same way for everyone. Human personalities and minds are too different for this to happen.
There are surely certain mental and emotional processes that are common to all people. However, people do not have the same mix of these processes -- one may be stronger than another in a given person, for example. Therefore, a therapeutic approach that works for one person would need to be modified for another person.
If therapy worked the same way for everyone, it would be much easier and quicker.
I think that the answer to such a question would be best answered by those preeminent voices in the field. Having said this, I think that there is strong evidence to suggest that each individual person responds differently to psychological therapy. The reason for this is that there are many different and contributing factors to the receptivity and effectiveness of psychological enquiry. A significant component of this is the patient's ability to embrace psychoanalysis or therapy as a way to address different issues within the psyche. I would also suggest that part of the effectiveness of therapy is the belief of what the concept of therapy is. If someone believes that therapy is meant to help better understand their own condition or state of being in the world, there could be vast difference than someone who seeks to be "cured." This mentality could also impact whether or not therapy works in the same way for everyone.