Two dates are generally contested here - 27 B.C. and 31 B.C. While the Battle of Actium was won by Octavian in 31 B.C., 27 B.C. is the year in which Octavian officially took the title of Augustus.

Rome certainly did maintain the facade of a Republic during Augustus' reign, and this was largely due to his careful crafting of his power and image. While the Senate did still have a lot of power during this time, make no mistake that Octavian was in control. In the end I believe that it's up to individual interpretation and how you would define an empire. It's certainly not an easy answer and it will never be a strict dichotomy - the transition from Republic to Empire was just that, a transition which took time and slowly evolved.