EDoF stands for Extended Depth of Field and works by using an asymmetrical lens that has the capability to focus objects from different distances, depending on which parts of the lens the various light 'rays' strike, on the same sensor.EDoF is a more common type of camera sensor today because it is cheaper to manufacturer, and doesn't require large spaces because of the absence of auto-focusing parts. Example of phones with EDoF cameras are Nokia C7, E7 , while phones with Auto-Focus are iPhone 4, Nokia N8, Sony Ericsson Xpera Arc
Although EDoF is more robust, quicker to take shots, better in video capture , that doesn't mean that its a better camera module for cameras. Actually, knowing what kind of scene or subject you will be shooting makes a difference in choosing which particular camera type would give better results.
Below is a list of 9 possible use cases for camera phone (there are still more but to make this post simple , just relate other scenarios that are closely-related with one on the list below) and an indication of when to use EDoF or Auto-Focus camera to get best output.
The list below also assumes that the subject or scene is well lit , as darker scenes require larger sensors.
And here is a video capture demo between an EDoF camera phone(Nokia E7) and an Auto-Focus camera phone (Nokia N8)
From All About Symbian