As a general observation, I find that the MBTI is very popular in professional development contexts such as team building. In contrast, the Big 5 is very popular in research contexts.
Several obvious reasons exist for this.
- MBTI is typically interpreted in terms of types rather than position on a continuum, whereas Big 5 is interpreted as a position on a continuum. Continuous models of personality are a more accurate representation of reality. Types are easier for people to understand and talk about.
- MBTI aims to have no "bad poles" and is based on a Jungian theory. The Big 5 aims to describe personality in a parsimonious way and has been empirically developed through large-scale factor analytic work. Thus, MBTI types are more acceptable to people, whereas the Big 5 has a degree of social loading on several factors, in particular this can be seen in neuroticism.
Neuroticism in the MBTI: The McCrae and Costa (1989) study that you cite suggests that neuroticism is poorly captured by the MBTI. Neuroticism is a very robust personality dimension capturing various tendencies to experience stress, anxiety, depression, and various other negative emotions. It is generally the best correlate of many well-being and life satisfaction measures. It correlates highly with many outcomes. Thus, I would find the absence of something like a neuroticism factor to be a major shortcoming of a personality test, particularly were it to be used for research purposes.
- McCrae, R. R., & Costa, 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.