if talking about equipment broken down, chiller system has 2 equipment to be worried (chiller & its pump) than fan.
Using fan = higher evaporation rate, thus ato is highly recommended.
Fan depends on ambient temperature to bring down 1~2 degC. Will need ice pack / ice bottle to bring it lower, especially in hot spell.
Hot exhaust from the chiller will increase ambient temperature, resulting in never ending cycle of heating / cooling.
Chiller running cost is higher than fan.
Appearance wise, chiller setup is neater and more "pro".
BTW, im a fan man for the past 2 years. In colder months, it can drop to 26degC. Hottest maybe 31degC.