It is comparing apples to oranges... But not in a bad sense!!
Buhner is thinking not in terms of energies (heat, humidity, stagnation, whatever used in Chinese medicine), but in terms of immune cells, inflammatory cytokine storms, rebuilding tissue lost to infections, he chooses herbs that cross the BBB in systemic ways etc.
The approach is totally different but I don't think one is correct, while the other not. Both are different ways to treat lyme.
Both use synergy of herbs in different ways.
If you go treat TCM, adding Buhner's herbs may mess the whole treatment.
If you go treat Buhner, maybe the TCM practitioner will not agree with certain herbs because they cool you too much, or whatever reasons he sees as causative of illness.
Buhner treats infections, immunity, damage.
TCM treats the whole body's energies, so that it brings back health on its own.
That is a bit too simplified, but I feel it's easier to explain like that...
Think that acupuncture is part of herbal treatment in TCM and you understand HOW TCM differs from approaches such as Buhner's or Cowden's...
Having said that, I know that TCM is also rich in antimicrobial herbs, so it may be not really that simple to 'separate' the approach the way I'm doing, but ... I hope something makes sense!!!