Are you asking if one notation is better than the other? It is just a question of definition whether the factor 1/2 is used or not: it depends on the authors. What you have to make sure is that the equations are modified accordingly.
EDIT: I just saw your second question. Depending on the definition of the strain tensor (with or without 1/2) you will recover the equations with "2 mu" or simply "mu" by multiplying or dividing by 2.