To put it simply and lightly, Ju is the teacher who wants discipline in the class whereas Me is the student who wants to play and does not want to listen to boring lecture and who hates discipline. But, there is much more to this.

Ju likes to see picture as a whole, whereas Me is interested in pixels forming the picture. In the language of optics, Ju is about the wave nature, while Me is about particle or quantum nature. Using Kinematics analogy from Physics, Me is about motion whereas Ju is about rest. In the language of Calculus, Ju is like a continuous function and Me is like a discontinuous function. Spiritually, Me is about duality (dvaita) while Ju is about non-duality (advaita). Ju is sattvic whereas Me is rajasic. Ju is knowledge and oration while Me is the transmission system through which knowledge and oratory is expressed.

Effective speaking involves both  faith + transmission mechanism.  This way, Ju and Me compliment each other perfectly. There are many areas like physics, commerce education, astrology, technical education, music (vocal, instrumental combo) etc. where Ju and Me work together.

The questioning and curious nature of Me completes Ju and the stillness of Ju completes Me. In this context, the difference in the two actually makes them complete each other. No wonder Gemini/Virgo the signs ruled by Me are the partners of Sag./Pisces, the signs ruled by Ju.