The MBTI can be considered to be subsumed by the Big5/Five-Factor Model. McCrae and Costa examined this back in the late 1980’s. First of all, they showed that the types do not interact in a statistically meaningful way indicating that there isn’t a reason to interpret four type categories (e.g., ESTJ vs INFP). The categories (e.g., extraversion vs introversion) describe some meaningful amount of variance themselves but combining them into the types and interpreting the whole is not statistically warranted (McCrae & Costa Jr., 1989). Statistically, false dichotomization/median splits (here called types) reduces the predictive power of a measure in general.
To further examine the universality of the Five-Factor Model, they examined how the MBTI dimensional raw scores related to the FFM/Big5 scores. They showed that FFM-Extroversion was highly correlated to MBTI-Introversion (r = -.74), FFM-Neuroticism was weakly correlated to MBTI-Introversion (r = .16), FFM-Openness was correlated to MBTI-Intuition (r = .72), and to MBTI-Perception (r = .30), FFM-Agreeableness was correlated to MBTI-Feeling (r = .44), FFM-Contentiousness correlated to MBTI-Perception (r = .49). These correlations were for men only, but are reported to give as an example of how the FFM can account for MBTI measures. The MBTI does not capture trait Neuroticism which could be considered a fault because Neuroticism is strongly predictive of many negative outcomes (Barlow, Sauer-Zavala, Carl, Bullis, & Ellard, 2014). The other factors of the MBTI are accounted for in the FFM, but captures additional variance above and beyond the MBTI. Validity and universality of the Five-factor model is another question but, briefly, it is empirically derived from factor analysis of the entire English dictionary (lexical approach) a factor structure which has been replicated in over 40 languages (McCrae & Costa, 2008).
Barlow, D. H., Sauer-Zavala, S., Carl, J. R., Bullis, J. R., & Ellard, K. K. (2014). The Nature, Diagnosis, and Treatment of Neuroticism: Back to the Future . Clinical Psychological Science , 2 (3 ), 344–365.
McCrae, R. R., & Costa Jr., P. T. (1989). Reinterpreting the Myers-Briggs Type Indicator From the Perspective of the Five-Factor Model of Personality. Journal of Personality, 57(1), 17–40.(https://www.researchgate.net/profile/Paul_Costa3/publication/20447534_Reinterpreting_the_Myers-Briggs_Type_Indicator_From_the_Perspective_of_the_Five-Factor_Model_of_Personality/links/00b49515b9ad847e86000000.pdf)
McCrae, R. R., & Costa, P. T. (2008). Empirical and Theoretical Status of the Five-Factor Model of Personality Traits. The SAGE Handbook of Personality Theory and Assessment: Volume 1 — Personality Theories and Models. SAGE Publications Ltd (pp. 273–295).