It may run less often, but it really depends on how much power it draws, to determine if it will be more or less expensive to run. You'd have to figure what the duty cycle of the two chillers would be (I don't know if the manufacturers publish how quickly they can cool down X gallons of water) and calculate the cost. Just remember, the chiller motor will generate heat, and the heat from the water is going to be dumped into your room, as well.
Honestly, a Kill-A-Watt would be a good investment in general, and could help you with this.
Have you considered fans blowing across the surface to aid evaporation (and thus remove heat from the water)? An ATO could make up for the evap loss easily.