What is the differance between microstep drivers and half/full step drivers?  The name implies one drives in micro steps, where the half full drives in one full step.  What are the advantages / disadvantages? 

Put simply, if a stepper is designed to step 200 steps per revolution, a micro stepper will make it step more. A micro stepper could for example make the same stepper now step 2000 steps.
Some advantages are smoother motion, higher resolution, and better mid range speed torque.