Socionics is more complicated, but its also more organized. I think MBTI is for basic understanding. They are both different but there is close correlation to types, not exact correlation, maybe one or two letters off. The functions/positions, relations, and terminology are what is really amazing about this Socionics theory. I love it a lot.
Basically there is a more effective way to estimate J/P types. A J type response is a direct reaction towards another while a P type response depends on the state of mind that had been influenced by others. Js also usually possess calm but long lasting moods while Ps usually possess shorter/stronger moods more impulsively. Js work toward their own view of the world, one that is growing closer to expectation, while Ps except aspects of the world and try to understand as much as they can. Each of these three divisions are logically connected to the idea of rationality and irrationality.