Overall air conditioners can cool a space more efficiently due to how the technology works. That isn't to say that fans can't accomplish a lot, because they absolutely can, but the key difference lies in how each piece of tech cools the air.
Fans circulate the air, creating a breeze which has a cooling effect, and the faster air can be circulated, the greater that cooling effect can be. Aspects like fan size, and RPM play a big part in how effectively a fan can cool a space, but the key measurement to look out for is CFM (cubic feet per minute), or CMH (cubic metres per hour). This number indicates the volume of air the fan can circulate within the minute, or hour, respectively. The higher this number, the more efficiently a fan will be able to cool the space, although not all fans provide it. We'd steer clear of those, but if they're more within your budget, look for something with a large blade span, and an RPM greater than 2000 for floor fans, or 200 for ceiling fans for the best cooling efficiency.
Air conditioning units on the other hand use a coolant to chill the warm air, before pushing it back out into the room. Over time the air within the room will be entirely replaced by the colder version, resulting in a greater cooling capacity. How well this works depends on the cooling capacity of the unit, it's efficiency percentage, and the room itself.
The cooling capacity is usually measured in kW, and how much you'll need depends on how big of a space you have. Picking the right size air conditioner is a crucial first step, but assuming you've already done that, the cooling efficiency is equally important. Cooling efficiency is usually a higher kW rating than the energy consumption, although that may not always be the case. Due to their heat pump technology, air conditioners are generally able to cool multiple heat units per watt of power used. A unit that can cool 3 heat units per watt of power will have a 300% cooling efficiency. The higher this percentage is, the better.