For me, psychodynamic is just deeper. CBT tries to change quickly problematic behaviour and psychodynamic tries to understand these behaviours, find a source of this and in consequence these behaviours, thinking, symptoms etc. disappears.
It takes A LOT of time and money - but for me, it's worth it.

For example - I used to have panic attacks in traffic.
As I understood, CBT is more focused on working with thoughts (that nothing bad will happen in this situation) or with desensitization (try to do this anyway, and finally you will use to traffics).
But after psychodynamic, where I can talk about my feeling, family, relationships - panic attacks disappear anyway (without trying and changing thoughts or being in this situation more often). I believe that then when I work through other important stuff my mind doesn't have to create other symptoms (like panic attacks, depression, insomnia, addictions).