The MBTI is widely used in applied contexts, such as for personnel selection. Nevertheless, it is hardly used in scientific research on personality because its theoretical basis questionable, because its validity is limited, and because its reliability is inferior to other established measures of personality (for a starting point to criticisms of the MBTI see McCrea & Costa, 1989 and this earlier post). For these reasons it is unlikely that you will find reliable data on gender differences in the MBTI.
However, it has been shown that the MBTI traits overlap with those of the Big Five (the most widely adopted model of personality) and gender differences with regard to the Big Five have been studied extensively.
The MBTI Judging dimension and its Perceiving counterpart overlap to a large extent with the Big Five trait conscientiousness (e.g., Furnham, 1996, McCrea & Costa, 1989). This is not surprising if you look at how Judging vs. Perceiving and conscientiousness are measured:
Judging vs. Perceiving is measured by having people choose between sentence pairs such as
- "I like to have things decided." vs. "I like to stay open to respond to whatever happens."
- "I like to make lists of things to do." vs. "I appear to be loose and casual. I like to keep plans to a minimum."
- "I like to get my work done before playing." vs. "I like to approach work as play or mix work and play."
- "I plan work to avoid rushing just before a deadline." vs. "I am stimulated by an approaching deadline."
Conscientiousness is measured by items such as
- "I get chores done right away."
- "I carry out my plans."
- "I stick to my chosen path."
Thus, there appears to be a clear semantic overlap between the two constructs.
Are there gender differences with regard to conscientiousness? According to a large scale meta analysis (with data from more than 23.000 participants from 26 nations, Costa et al. 2001), 1. there are far more personality differences within the genders than between genders 2. for conscientiousness there doesn't seem to be a detectable gender difference.
Costa Jr., P., Terracciano, A., & McCrae, R. R. (2001). Gender differences in personality traits across cultures: Robust and surprising findings. Journal of Personality and Social Psychology, 81, 322–331. doi:10.1037/0022-35220.127.116.112
Furnham, A. (1996). The big five versus the big four: the relationship between the Myers-Briggs Type Indicator (MBTI) and NEO-PI five factor model of personality. Personality and Individual Differences, 21, 303–307. doi:10.1016/0191-8869(96)00033-5
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, 17–40. doi:10.1111/j.1467-6494.1989.tb00759.x