I think it is extremely important to know how you come across to other people. Not because you need to change who you are, or because other peoples opinions are more important, but because people react to how you come across them. Not to how you really are.
So if those 2 are out of balance, people are not dealing and reacting to the "real" you, but to the image they have off you. That might not always be a bad thing, but I believe it is always a good thing to be at least aware of it.
One example of my personal life:
Back when I was extremely shy, I got the feedback from a friend at one point that when she first met me, she thought I was extremely arrogant, and believed I was better then anyone else. This was my self defense mechanism. I thought I was pretending to be self confident, but what the outside world saw was arrogance.
In this case I changed some minor things, and came across very shy, instead of arrogant. Since that was closer to my true nature, I preferred that, to being perceived something that I wasn't at all.
A good way to know what people think of you: do a 360 evaluation.
This is asking all the people around you, meaning Boss, people under you professionally, family, friends etc. what they think of you. What do they think is your strong side and what do they think you would do well to change.
When you read them (especially good to do with an impartial 3rd party therapist for objectivity) keep in mind that this is not who you are, this is how others perceive you.
Before you read and analyze their messages, make a list of yourself. Who are you really. How do you want to be perceived by others. By friends, by family etc.
Then see how far those things are in line. If they are, good. You are being perceived the way you want to.
if not, ask yourself why, and if it is something you want to change or not.
Hope this answer helped!
Lots of Love,