Hi Karmamechanic:
There is overlap in effects between asanas and tai chi, but there is a distinction. Tai chi is mostly grounding with some inner opening, while asanas are mostly inner opening with some grounding. This is why tai chi is good for helping to stabilize energy difficulties, and asanas are a good preparation for sitting practices, including spinal breathing pranayama and deep meditation.
As for breathwork during asanas, it is not specifically recommended in AYP, due to the possible “doubling up” effect with spinal breathing and other pranayamas used in sitting practices. Too much pranayama (with possible delayed effect) can lead to excessive purification and its associated physical and emotional discomforts. In AYP we suggest gentle awareness of natural breathing and body positions during asanas. We also have a samyama method that can be used as an alternative during asanas with good results – it is provided in the AYP Samyama book.
All the best! 
The guru is in you.