I myself am somewhat introverted but feel I'm fairly high on both of those points. I have a friend who is very extroverted who I would say also scores well on both of those points but the main difference between him and I, he just seems to do or say things without much thought beforehand and sometimes comes to regret it later. I've always thought impulsivity may lead to more extroverted people and inhibition to more introverted people.

I think there are different levels and I'm pretty sure that a lot of people who think that they have really good self awareness actually don't.

You need to be exposed to a lot of difficult and unusual situations in order to learn about yourself. Also you need to be honest with yourself because most people have a habit of post rationalizing their behaviour as a way to maintain labels like "I'm a good person", "I'm a winner", "I'm smart", etc... People who subconsciously try to assign labels to themselves usually don't have good internal self awareness because labels are the product of external advertising; it's an externalized/socialized way to think about yourself...

Guess I'll have to take your word for it as I must be too self deluded to see otherwise :).

Edit: I'd also like to add that as someone who meditates daily, I actually disagree that being exposed to a lot of different situations is automatically going to help you get to know yourself better. You can be exposed to all sorts of situations and not be mindful of what is going on inside. Alternatively, you can be doing something totally mundane like sitting and watching your breath and come across new and interesting things going on in your own mind that you had never noticed before. The difference is going to come from how mindful you are.