Gold has utility besides its currency value; it's easy to work, highly conductive and non-reactive, making it ideal for many industrial and aesthetic purposes.

Paper currency is backed by a government promise. Of course, if people lose faith in a state or a government persistently debases the fiat currency, people will lose confidence in it. But as I've pointed out before, while there have been many hyperinflationary episodes, it's not that frequent of a problem relative to the number of countries and currencies in existence.