None of the three are necessarily more efficient.
Dry steam versus flash steam depends on the conditions under the ground. How hot is it down there? If hot enough, the fluid comes out of the ground as steam. If cooler, it comes out as hot water.
The biggest design decision for a geothermal power plant is how to deal with minerals and contaminants in the steam. Have you ever tried to taste the water that comes up in a geothermal spring?
Contaminants foul the turbine blades and cause the efficiency of the turbine to degrade over time. Other components, heat exchangers, flash tanks, and piping can also be fouled by contaminants. Sometimes that requires frequent shutdowns to clean the components.
The binary cycle type of plant includes extra equipment and extra cost to make sure that the steam through the turbine is clean and free of contaminants. Still everything on the primary side of the heat exchanger needs cleaning, but that's easier than cleaning the turbine.
So the short answer to your question, is that cycle efficiency in a geothermal plant is not as important as dealing with contaminants.