Well neither really. We would tend to say: I set out to become a doctor. You might on occasion be able to say you have set out to become a doctor, but the continuous tense is wrong, because you are not resetting out every day to become a doctor. You only start the process once.

The second usually refers to past action. Eg: "I am writing a novel" = I am currently writing a novel "I have been writing a novel" = I have been writing a novel for some time. But it does not necessarily mean that you are still doing it. "I have been writing a novel, but recently I have been so busy at work that I have not had time to write." It is a little odd to say "I have been setting out to become a doctor," but it is not wrong, because it could make sense in context: eg, you have taken biology classes, have studied for the Medical College Admissions Test, etc. In other words, you have taken several steps required to become a doctor.

The two sentences are equally perfect, and their meanings are very close. The only small difference that exists is one of emphasis. Technically, the meaning of the sentences is as follows: #1) "I have, as an experience, 'setting out to become a doctor'. #2) "I have, as an experience, 'being described by the adjective phrase 'setting out to become a doctor'". So, #1 describes an experience of "setting" (doing something), while #2 describes an experience of "being" a certain way. Neither sentence creates any timeframe. Either could be describing a situation that existed 10 years ago. Without context most people will interpret the sentences as experience that continues to the present moment. In brief, the difference is between action (#1) and description (#2).

To set out means to start. It is not a continuous action, so the second sentence is wrong.