Clearly, these major types of therapy are quite different in their assumptions and approaches, and none of them is appropriate for every individual. To a certain extent, the decision of which to use may be indicated by the nature of your problems. People who have a long history of recurring major depression, very severe depression, or a combination of major depression and other chronic mental or physical health issues to contend with, may not be able to benefit as much from a short course of Cognitive Behavioral Therapy, and may need longer term treatment. Your therapist can help you figure out this aspect of the decision.
But it’s also important for you to feel like the treatment you receive is relevant and helpful to you, and to have a voice in deciding what kind of approach you want to try. You’re the one who will have to do the work, after all. Hopefully, this information will help you make the best decision.