From what I understand, the psychology behind trait theory is still being developed, but the Big Five represents the best model that we currently have. Even for psychologists uncomfortable with rigid personality characterization (for good reasons), the Big Five can still be seen as some of the basic building blocks of human temperament.

Introversion/extroversion is in both, but while in the MBTI it's a binary identity (as this article seems to posit), in the Big Five it's a spectrum that is close to normally distributed.