If we were to split up the practitioners of psychotherapy into to distinct groups, I think that one criterion that splits them might have to do with the relationship the therapist has with emotion. Better said: Will the facilitator allow himself or herself to feel with/due to the client? Feeling takes real energy from the practitioner that can manifest later or can crop up outside the relationship. It could also be a subjective marker for the client. Does feeling help the therapy process? Perhaps feeling leads to ethical dilemmas. Many of those sound, negative but assuredly there is much that is positive here.
As far as different theories are concerned, I think that we can all agree that fundamentalist clinicians, if such a thing were to exist, would come down on one side of this argument. More humanistic practitioners would describe the importance of being in the moment with the client, experiencing what they are experiencing to some degree. More cognitive therapists, by nature, would eschew such tactics and really heavily on the thought process of the client. Both the nature of the therapy and role of the clinician as expert would not really allow the therapist the space to identify the clients/their own emotional circumstances.
Were the therapist to allow himself or herself to feel, would there be any negative side effects in the session? Sure, emotions can be distracting. The clinician must not only track and pursue the emotions of the client, but must also keep a tight hold on his or her own feelings. These could cloud the counselor's judgement, disallowing good therapy to occur. It is very possible that, based on a clinician's own past, an intervention could fail. Feeling also takes up energy that the therapist could use thinking, filling out paperwork, or relaxing.
The client must e taken into account as well. Does he or she respect the emotional spectrum? Is there a previous diagnosis that precludes accessing emotional data? Just as the style of therapy should match the therapist, of course that same style should match the client. There are some who either militantly do not wish to access their emotions, or are so cognitive that emotions play little part in their lives. With these clients, showing what the therapist feels would be uncomfortable and, for them, almost bordering on inappropriate.
Feeling emotions is one thing, but showing them is altogether different. While the argument for or against showing emotions is not over, I'd like to cover this. Some clients would like the therapist to show some kind of emotion - this could vary from a slight pinching in the eyes in empathetic pain, to openly weeping. Personally, I would say that the former is better than the latter. There are some clients that might take advantage of the therapist of the latter emotional persuasion. Covering up emotions can also take up important time and energy that could be used for other things.
Opinion time: I am an advocate of the therapist feeling in session. There are some definite negative possibilities to the equation there, though. A therapist can choose to act on the feelings, engaging in either predatory, maleficent, or sexual acts with the client. This probably isn't the best option. Some other negatives are listed above. Emotional therapists can also use their feelings as tools. They can deduce, though their own state, what the clients if feeling. They can also attempt to use this superpower to try to predict behavior.