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By BPD, I think you are referring to Borderline Personality Disorder. This disorder can cause people enormous amounts of struggle and pain in their personal relationships and can also lead to feelings of emptiness, depression, and extreme low self worth. People with BPD often try to alleviate these painful feelings by connecting with someone in a very close relationship, but fairly quickly feel that this person is disappointing them and is not alleviating their negative self-feelings at all. This can then lead to relationship conflicts.
Bipolar Disorder is a mood disorder that also causes feelings of depression, as well as the feelings of mania and euphoria and/or irritability that I'm sure you are aware of.
While both of these disorders can cause problems for people, I wouldn't say that either is more serious than the other. Bipolar disorder can be managed with medication which often alleviates symptoms to a large degree, whereas medication has not historically been as effective for people with BPD. Usually people with BPD benefit more from a combination of individual psychotherapy and group psychotherapy- especially a form of therapy called Dialectical Behavior Therapy, or DBT.
I would suggest that you continue to work with your psychiatrist to find medications to manage these disorders, and maybe also look into finding a DBT therapist in your area. Your psychiatrist might be able to recommend someone.