There have been multiple studies comparing the effectiveness of manual brushes as opposed to electric brushes.
Although not all the electric brushes are the same, in conclusion of all these studies it is fair to say that in general electric brushes are more effective in controlling the plaque than manual brushes. Theoretically you could do a very good brushing with a regular hand brush but the movements of an electric brush makes the task easier and more efficient. Also, some electric brushes (Sonicare) have sonic vibration that is difficult to mimic with a hand brush! Other electric brushes like Oral-B and Rotadent have small heads that help you reach hard to reach areas of your mouth. This aspect is more important when you are talking about somebody with orthodontic braces or a history of gum disease.