What useful information can I get from ASH report which I cannot get from AWR report?
AWR(Automatic Workload Repository Reports) takes snapshots of the database in specified intervals(one hour is default) and stores that data for later analysis. For example continuous improvement of the database work.

ASH(Active Session History) has information about current active sessions, and it gather data every second. If you are experiencing sudden database issues, you should use ASH.

More on this subject
http://docs.oracle.com/cd/E11882_01/server.112/e16638/autostat.htm#PFGRF94186