There are no extra features or abilities for Head Teacher or Director, besides having different email notification settings. 

Setting someone as a Head Teacher or Director allows you to label someone with that position at your service. 

One thing you can do, is allow the Head Teacher or Director to receive emails for new Parent Stories and Comments (for their profile children), separately from other teachers.
To enable or disable emails for Parent Stories and Comments, access your Site's Notification Settings and either tick (to enable) or un-tick (to disable) the following settings: 

More information on your Site's Notification Settings - Click Here

Did this answer your question?