Syrups tend to be runnier then a sauce. The sauce also changes the texture of the drink too. IMO it makes it smoother. There are some people who only use sauces and other who only use syrups. Its really a personal opinion. Sauces have a tendency to make the drink a little on the rich side. But people seem to like drinks that way.
Really though you need to try them both ways and see how you wish to make them.
Syrups and sauces can be used in both hot, cold, and blended. There pretty versatile that way. A thicker sauce will require to stir it all in but it should be just fine. I know a few places that add the Ghirardelli Chocolate Sauce to ice cream drinks before they blend it all together. Very tasty.
There are smoothie and frappe mixes available for blended ice drinks that are formulated to work in the colder drinks.