I have used cognitive techniques related to CBT, mindfulness and NLP as coping strategies since my teens (although didn't always use those terms for them). They work to the extent that they enable me to get by most days and stay in work/life. But they do not go any further than that or deal with the affective and dysfunctional attachment based core of my problems. For that a more psychotherapeutic approach works better.

However I would not see this as an either/or thing, and also there are actually more treatment modalities than cognitive vs psychodynamic/psychoanalytic anyway. There are numerous psychotherapeutic approaches, the psychodynamic tradition itself has many strands and more recently has started to move closer to a more scientific understanding of the role of attachment and affect dysregulation so we are starting to see approaches emerging that are more science based and uniting developmental neuroscience with therapy (and there are also techniques like EMDR that tap more into the neuroscience part but less the psychodynamic part). Alongside these there are also humanistic approaches that tend to focus on the therapeutic relationship but more in the here and now and discourage transference and the formation of dependency relationships. Last but not least there are activity and creativity/drama based approaches that I find particularly helpful as there is much more to therapy and healing than words alone can accomplish.