There are both differences and similarities between Apollonian/Dionysian and Yin/Yang. They both deal with opposing forces and are methods of trying to explain how this world works.
But the differences are bigger than the similarities, in my opinion.
First of all, the definition or concept of Apollonian/Dionysian is far more squishy than Yin/Yang. Whereas Apollonian/Dionysian can work in harmony, it often doesn't. Yin/Yang always does.
Second, in Yin/Yang, Yang is seen as active and Yin is seen as passive. But in Apollonian/Dionysian, neither is passive, both are very active forces.
The reason I bring this up is because our culture is influenced by both and they may overlap, but they are not the same. In my opinion, Yin/Yang is the more honest and steady of the two with very specific and stable definitions.
But even so, my main point of going down this road is to point out that these are HUMAN constructs and thought patterns. They are systems created by flawed humans to help them deal with a fallen world. They are not biblical. They are shifting sands offering no solid foothold.
Though we can acknowledge the thought patterns and even appreciate art and music concerning the human condition that use these elements to paint a picture, as Christians, we are not to place our trust in these elements.
We have a solid Rock, Jesus Christ, on which to built our spiritual home. All other ground is sinking sand.
Knowing this and seeing the Apollonian and Dionysian infiltrate church thinking is what has prompted me to bring this to the attention of others which is what I hope to do in the next few weeks.
(Link to Wikipedia for definition of Yin/Yang just FYI)