Generally, given freedom of choice, you would feed a delta load from a star source. Sometimes that freedom of choice isn't open to you, either because something already exists and you're connecting to it, or because you have to match phase displacement, etc.
The main problem with two delta systems is the lack of a reference to earth which makes it harder to provide protection against faults, and the phase-earth voltages can reach the full line-line voltage creating higher stresses on insulation than would exist in a grounded system. Two stars interconnected brings all manner of peculiarities. They are discussed at length in The Whys of the Wyes.