Ashes to Ashes
This is the more visually appealing one. I should note that it is NSFW and French. Here is what their site has to say about it
Ashes to Ashes is an unofficial short film shot in 13 days and postproduced in France between 2006 and 2008. This fan film is based on the Batman character created by Bob Kane and on the graphical universe of Franck Miller’s Sin City. Original screenplay by Samuel Bodin and directed by Julien Mokrani & Samuel Bodin.
City of Scars
I can't find as much information on it.
When the Joker escapes from Arkham and murders the parents of a young boy, Batman recalls the pain of losing his own parents as a child. He is pushed past his limits to the point where his focus becomes revenge on all who stand in his way, including many of Gotham’s underworld. Finally, Batman is forced to look at the psychological profile of his own mind and except the consequences of his life to find resolve.
Written and directed by Aaron Schoenke, the short was filmed with High Definition cameras over 21 days with a budget of only $27,000.