To a degree, all psychotherapy is depth psychotherapy. I say this to mean that every therapy is going at least slightly beneath the surface in order to bring to the client's attention that there is something going on that is affecting their behavior negatively. What the therapist is looking out depends on their orientation, but all at least go beneath the surface a little.
We can, though say that some are deeper than others. Some theories, such as pure existential theory is 100% depth-oriented. There are, of course, advantages and disadvantages to this. I believe that I have talked about this earlier and do not wish to rehash that topic. What I would like to talk about is a non-depth-oriented theory here. It is funny to me when therapists guffaw in the face of depth-based therapy.
It seems to me that going beneath the surface to thoughts is good, but not enough. It almost seems lazy. One can infer much from thoughts and belongs in a deeper therapy than CBT because the therapist is inferring much from the thoughts (it also goes to show how difficult it is to be a raw CBT user). It behooves the client to get to know themselves on a deeper level. Only at this point, in my opinion, is it possible to truly identify normal or maladaptive behaviors and then change them in the moment.
I must say that there are therpies that do not go beneath the surface. I personally would not call these psycho-therapies anyway. These include (but are not limited to) behaviorist therapies and neurological/medical therapies. Neither of these care to go beneath the surface or engage in a meaningful relationship with the client.