The choice of fans or air conditioners to cool a home is a matter of preference, but using fans alongside air conditioners is one of the better ways to tackle the problem. Fans help even out any temperature gap between floors, allowing a lower thermostat setting to cool both.
Ceiling fans on their own don't cool down a room; they just make it feel cooler because of air circulation against the skin. Cracking an upstairs window, along with one downstairs on an opposite wall, creates a draft, which helps with ventilation and puts less stress on the air conditioning unit.
A better solution is to install an attic fan along with a vent system to cool the attic. Enclosed attics are heat traps; if there is no place for that heat to go, it seeps into the upper floors through the ceiling. By installing soffit fans along the eaves and exhaust fans along the roof, cool air is drawn into the attic, which forces the hot air out. An attic fan accelerates the process and help cool the upstairs floor.
If adding fans to the air conditioning system isn't an option, creating cooling zones and installing two thermostats also works. A series of dampers, relying on signals from the two thermostats, opens and closes dampers as needed. The ultimate solution is installing two separate air conditioning units, but that is a more expensive option.