What is the advantage of differential Manchester
According to wiki answers: -


  Unlike with Manchester encoding, only the presence of a transition is
  important, not the polarity. Differential coding schemes will work
  exactly the same if the signal is inverted (wires swapped).


That sounds a nice feature to me.

On another wiki answer it says it gives better noise immunity than normal M-encoding. And on another it explains how it achieves it: -


  A '1' bit is indicated by making the first half of the signal equal to
  the last half of the previous bit's signal i.e. no transition at the
  start of the bit-time. A '0' bit is indicated by making the first half
  of the signal opposite to the last half of the previous bit's signal
  i.e. a zero bit is indicated by a transition at the beginning of the
  bit-time. In the middle of the bit-time there is always a transition,
  whether from high to low, or low to high. A reversed scheme is
  possible, and no advantage is given by using either scheme.


Following a little trawl on the web I thought I'd put this drawing in that I modified to show how the bit transitions indicated logic 1 and logic 0 data: -



This is why the data stream can be inverted and you can still decode correctly.