Should I control the high power LED or its driver?

The drivers are no doubt constant-current drivers - this means their output terminal will rise to whatever voltage will yield that current through the LED or LED-string. This voltage is not very well defined (depends on power supply voltage, LEDs, temperature...)

So I'd suggest using the darlington transistor to switch power to the driver (low-side switching), since then we know the voltages will be what we want (emitter at ground, base via resistor to Arduino pin, collector to negative supply to driver...