Although they might look similar on the outside they are very different on the inside.  Long time desert residents say that about $10 worth of electricity for an air conditioner will cost about $1 with a swamp cooler.  The high temperatures of the desert and low humidity make the swamp cooler the item of choice, at least for much of the year.  The only exception will be during the high humidity months of July - September when the seasonal monsoon brings moist and hot air. 

AC works by passing air over a set of coils filled with a refrigerant chemical that heats and cools as it's compressed and expands. Coils cool down, air is passed over them, it gets cool and it is sent into the house.  AC is a closed system; it will need to work harder if you leave a door or window open.  The process of compressing the refrigerant takes lots of electricity.  That makes AC expensive.

Swamp coolers are very simple in design.  Water is pumped to a system of fibrous filters and a powerful fan pulls the outside air through the filters, the water evaporates in the process, and the same fan pushes the cool air into your house.  They work very well in the desert whenever the heat is accompanied by low humidity.  Swamp Coolers are an open system, you much leave a door or window open for the air to circulate in the house.  Swamp coolers also use just a fraction of the electricity that AC uses.

The average fan uses about 100 watts per hour while an AC unit uses 1200.  Fans work by increasing the rate of evaporation. When it's hot outside, our bodies sweat to maintain our core temperatures. As the sweat evaporates, it takes some of our body heat with it. If the air around our bodies is still, it becomes saturated with water. The more water in the air, the slower our sweat evaporates and the hotter. A fan moves the air around and constantly exchanges the water-saturated air around our bodies with fresh, dry air. This allows evaporation to happen more quickly so we feel cooler. Again, fans are most effective on days with low humidity.

Fans do not really cool a room, they just cool you, because of the evaporation from your skin.  So fans are not effective at cooling an entire house, for example, but they are a very effective way to cool YOU, particularly if you are in one location, like working at a computer or otherwise staying in one location.

The Sun is a unbelievably powerful source of heat in the desert.  It is estimated that 40% of unwanted heat comes through the windows of a home in a temperate climate.  In the desert, a single window with the sun shining through can significantly raise the temperature of an entire home.

In the winter, having a few windows that pass direct sunlight into your home can keep the entire house warm and save you lots of money in the process.  And on the flip side, keeping the sun out in summer can keep your home cool and save you even more money.