Do we recognize ourselves better when we see our mirror image? A friend of mine recently noticed that we both have a birthmark on the face. He looked at me and said that we have exactly the same mark. But he has it left and I right. But, when looking in a mirror, we see it on the other side. 

So, I wonder: Do we recognize ourselves better when we see our mirror image compared with e.g. a video of ourselves? Where is this studied?
Bredart (2003) discusses your exact hypothesis and reports the results of a couple of studies. I'd recommend having a read of the article.

The authors acknowledge that in contrast to familiar others the experience of our own face typically comes through self-inspection in mirrors. 

They summarise some relevant literature:


  Troje and Kersten (1999) showed that participants were faster when
  naming frontal views compared with profile views of their own face,
  and that this advantage for frontal views disappeared when naming
  familiar colleagues’ faces. In addition, Laeng and Rouw (2001) showed
  that the full-frontal view is superior to other views for facial
  self-recognition but not for the recognition of other people’s faces.
  A pose corresponding to 22.5 degrees from the frontal view seems to be
  optimal for other people’s faces. However, for highly familiar faces
  (e.g. faces of close friends or partners), the frontal view could be
  recognised as quickly as the 22.5 degrees view. In short, because of
  ecological constraints on visual experience, self-recognition is
  easier from frontal views than from other views. This superiority of
  frontal views was not observed for other highly familiar faces.


They also discuss one methodology that involves "searching for a target face among a set of other faces". Thus, the speed of finding the face is one way operationalising familiarity.

With regards to their findings, the following quotes the abstract:


  Experiment 1 examined our ability to recognise the usual horizontal
  orientation of our own face (mirror orientation) as compared with
  another very familiar face (normal orientation). Participants did not
  use the same kind of information in determining the orientation of
  self-face as in determining the orientation of the other familiar
  face. The proportion of participants who reported having based their
  judgement on the location of an asymmetric feature (e.g. a mole) was
  higher when determining their own face’s orientation than when
  determining the other familiar face’s orientation. In experiment 2,
  participants were presented with pairs of manipulated images of their
  own face and of another familiar face showing conflicting asymmetric
  features and configural information. Each pair consisted of one
  picture showing a given face’s asymmetric features in a
  mirror-reversed position, while the facial configuration was left
  unchanged, and one picture in which the location of the asymmetric
  features was left unchanged, while the facial configuration was
  mirror-reversed. As expected from the hypothesis that asymmetric local
  features are more frequently used for self-face judgements,
  participants chose the picture showing mirror-reversed asymmetric
  features when determining the usual orientation of their own face
  significantly more often than they chose the picture showing normally
  oriented asymmetric features when determining the orientation of the
  other face. These results were explained in terms of competing forward
  and mirror-reversed representations of our own face.


Reference


Bredart, S. (2003). Recognising the usual orientation of one's own face: the role of asymmetrically located details. Perception, 32, . DOC
Laeng B, Rouw R, 2001 “Canonical views of faces and the cerebral hemispheres” Laterality 6 193-224.
Troje N F, Kersten D, 1999 “Viewpoint-dependent recognition of familiar faces” Perception  28 483-487.