If a device takes in a range of voltages, is there an optimal choice of voltage to supply?
The LED light you have is a Blackbox. We do not know the configuration of the LEDs (if there are multiple). The power supply internal can be a buck regulator, or even a buck boost regulator.  

The LED driver IC type is also unknown. It can be probably a flash LED driver (example: STCF05)


Operating a device with minimum voltage with boost regulator will increase power dissipation across the coil due to increased switching current
A device operating at maximum voltage limit may have to dissipate more power across the regulator depending on the topology
Independent of the input operating voltage the LED luminance intensity will be almost constant
As suggested, it is also good idea to measure the input current and various voltages to understand about the power consumption
Go with the datasheet. If there is a test voltage mentioned while specifying the parameters or even a typical voltage mentioned, that will be the best point to start with.
If possible, even temperature can be monitored over time with fixed load condition but your mileage may vary