You could look at the Common Factors theory. It proposes that "common factors" shared across orientations (things like empathy, bond, congruence, ect.) account for much of the positive gains for clients in therapy. However, it also states that it is important that the therapist be integrating these factors into a therapeutic orientation. Not a model, but Edwin Bordin's foundational article on the therapeutic alliance, The Generalizability of the Psychoanalytic Concept of the Working Alliance, can give you information about how theoretical orientation places different demands on the therapist and client. I found a copy published in the journal Psychotherapy: Theory, Research and Practice Vol 16 issue 3, Fall 1979. Good luck!
The work of Scott Miller, Ph.D. and colleagues has indicated that the theoretical orientation contributes only a small amount of variance compared to the relationship between the patient and therapist. David Kraus, Ph.D. has also published findings on the effectiveness of individual therapists vs. the theoretical approach used.
The area that has not been sufficiently considered is whether certain characteristics of the patient would be associated with better outcomes with certain approaches than others. For example, would someone require encouragement for making changes do better with a motivational enhancement approach than CBT? Would someone with a substance use disorder and a lack of social network do better with a peer-support system such as 12-Step programs provide than MI or CBT? There have been some tantalizing indications that that might be the case, but there is a lack of dedication and sophistication in exploring differential results based on patient characteristics.
Dr. Bruce Wampold's work is also worth reviewing. His recent book published with Dr. Zac Imel is excellent: Wampold, B., & Imel, Z.E. (2015). The great psychotherapy debate: The evidence for what makes psychotherapy work (2nd ed.). New York: Routledge.
I was bout to recommend The Wampold and Imel book mentioned by Simon. It provides a very excellent overview of psychotherapy research, making the convincing argument that there is no evidence for the superiority of one set of techniques or brand of psychotherapy over another. In my view, there is something more fundamental at work in therapy than technique: how responsive is the therapist's intervention or attitude to the patient's particular problems and needs. Of course, determining what the patient needs is not always easy but our research group has worked on developing methods for doing so with very good results. The attached papers gives more detail.
Article How Patients Work On Their Plans and Test Their Therapists i...
Article Improving the yield of psychotherapy research