yes, the responsiveness depends on the ldr you are using. so i would rather build a circuit that can boost or attenuate the incoming signal before it hits the LED in order to get the desired response.
in your case (with the circuit i described in the initial posts) if you change the resistor to VDD you can alter the range(or more precisely the behavior) quite a bit, so try to use a 1k resistor and add a pot of 10k in series.