Allegories refer to any piece of writing which have a hidden message. The hidden message most often refers to one of a political or moral nature. Hotel Rwanda, a movie about a man who shelters hundreds of people from mass genocide in Rwanda explores the themes of genocide and taking charge for one's own safety. It is an example of allegory.
A commentary on the other hand refers to a piece of writing or visual which offers opinions about a specific topic or tries to explain a certain phenomenon in greater detail.
The similarities between the two are: they both deal with factual instances, they are both serious in nature.