I think people mostly switch when they hit a dead end with one kind of therapy. The answer to your question is not easy and depends on you and your problem. It's not like any of these therapies have the kind of scientific basis that, say, use of antibiotics does for particular infections. I think at this point if you have a good therapist who is ethical and experienced and meshes well with you, the particular therapy (assuming it's approved by some governing body) is not that important.

In short, some people think that it's all about you and how you see your problems. If you want to locate your problem in childhood, CBT is useless. Psychodynamic is the choice. But some might say it doesn't matter how you see your problem, that there is an objective way to decide what your problem is and how to help you get better. In that case, assuming CBT is determined to be helpful to you (by some objective standard), your refusal or frustration with it can only be seen as your resistance.

Regardless, if you have the money and time, it never hurts to get an opinion from a good therapist with a different orientation. But eventually you need to settle. Don't go jumping all over the place. That'll get you nowhere. My 2c