This should work. It won't have a huge amount of gain like an IC comparator.
VCC can be 5 to 9 volts, VEE can be -5 to -9 volts.
Balance it by placing the LDRs side by side and adjusting the pot until both LEDs glow at half brightness.
It is designed to deliver about 10ma to whichever LED is on.
If you need more gain, let me know and we can add another gain stage (it will be made of PNPs).
If you can't get 2N3904s, you can use almost any general purpose NPN.