I've done both psychodynamic and CBT therapy…

In a nutshell, psychodynamic therapy looks at the root causes of your issues and it can dig pretty deep, your family, childhood etc come up. Also, the relationship with your T may or may not be a focus. It is believed that you bring your relationship patterns with you and unconsciously play them out with the therapist

CBT is very "here and now" focused. Very specific tasks are given, large problems are broken down into manageable acts. I have found it useful for anxiety/phobia related things, regulating my health etc. I would never call CBT "deep" but I find that it gets results pretty quickly.