actually your questions mixes up two dimensions: extroversion vs introversion and thinking vs feeling. Hence there is no "extrovert vs a thinker personality" as your question suggests. Extroversion vs introversion and thinking vs feeling are character traits which come with specific behavior/preferences, i.e. you prefer specific work settings better than others or you like to communicate differently if you are more of a "thinking" than a "feeling" type of personality. However, you can succeed in consulting no matter what your personality type is - but it is easier to succeed if you know yourself and understand why others may prefer other working modes because you can adjust accordingly.
At Oliver Wyman, consultants' personality is analyzed in order to leverage your personality’s specific traits and to strengthen your relationships through better communication and understanding.
There are numerous web resources you can find that translate your personality type into "personality colors" and explain what it means in terms of your preferences/ how you can use it to your advantage.
Hope that sheds some light.