I know Superman predates Batman as far as first appearances in the comic books (1938 v 1939), but as far as the different universes go its not clear to me which character started vigilantism first. For example, in the new DC cinematic universe Superman started flying presumably after Bruce became the Batman. According to what has been said about the Dawn of Justice movie, Bruce will be the older Batman who has been around a while.
So who came first, Superman or Batman? I am more interested if they have mentioned this in the comics than the movie universes, but curious about both.