The EHIC mainly covers emergency medical and dental care and does not cover, for example, repatriation in the event of illness or accident, costs for hospital treatment that is not deemed necessary, or costs for private healthcare. 

Private travel insurance is more comprehensive and provides broader coverage and may include more benefits such as baggage delays, medical and hospital costs, travel home in case of illness or accident, and other types of assistance and compensation during the trip. So, the difference between the EHIC and a private travel insurance is mainly in the scope of the protection and the various benefits included.