When using shadow mapping, the resolution of your shadow buffer is lower than your default color buffer resulting in a low resolution shadow. But, this effect can be somewhat mitigated by programatically computing your light projection matrix so it covers the minimal volume possible.
In the above images, the buffer of the shadow resolution is the same. But, the bounds use for the computation of the light matrix (light_projection_matrix * light_view_matrix) differs. For the high res shadows on the right, the light projection matrix is controlled by the bounds of the view frustrum. In terms of a directional light, this will be an orthographic matrix, and the bounds of the light be the bounds of the viewing frustrum (which can be perspective or orthographic). This makes the resolution of the shadows far more high-res as only a smaller portion of your scene is considered. So, if you choose a reasonable resolution and use a bounds-aware light projection matrix you get good use resolution of your shadows. This can vary for level of detail that you shoot for based on the zoom of your camera.
Caluadewa Tharindu Mathew's Website 