My tour guide friend, Angel, a native Ecuadorian from Guaranda, has lived in Quito a lot longer than I have (which is a little more than a year).
He informed me that orange-plated taxis are registered and safe. White-plated taxis are not registered, therefore risky.
From my observation, all registered taxis are also totally yellow, most with a number on top of the roof. The fancy ones with black (or red or green) trunks, hoods and wide stripe on the sides all come with the white plates. Also, those that are called Executive have white plates. Avoid the white-plated taxis, especially at night.