The disadvantages of the Brushless DC Motor over the AC motors are:

higher maintenance (due to brushes)
more expensive
In addition to the above the Brushless DC Motors have the same advantages over AC motors but they also have more advantages over Brushed DC Motors

lower maintenance (no brushes)
even higher starting torque ( Due to rare earth magnets)
even higher efficiency (over 90%) on sub fractional motors
even more compact design
better heat dissipation
lower noise