If you try to observe organizations: you see that there are different leaders around. As a general classification, a leader can be more of an extrovert, while to the other extreme, a leader may tend to be an introvert. Each has different strengths, different weaknesses. But they can all be successful as leaders: IF, that is if they deliver results.
But if one fails to deliver on the results expected, no matter how charismatic one may be--you will easily find your way to the door.
All else being equal though,one may ask, which leadership style is best... The answer... The extrovert.
Leadership Position: Basic Requirement
Being in a leadership position requires leading and managing a group of people. This requires interaction with different personality types. This usually requires socialization, and small talks. If a leader is an extrovert, he or she may easily do this with ease.
If he or she is an introvert: social interactions become a problem. And this limits a leader's influence which is not what we want.
Being an extrovert will be an edge in leadership positions. Introverts are better off with other types of jobs, rather than in leadership positions. But if an introvert can improve the way he interacts with people, then things can get better.
Hope for the Introvert Leader
It all boils down to how an introvert will adapt to what is required of being a leader. If the introvert leader can make adjustments so that he or she can relate better with others, then the degree of the problem is put to a minimum.
Putting it in Perspective
However, not all extrovert leaders are better than introvert leaders. There are more things that a leader needs to have than having social finesse...