This one has two disadvantages.
1. there is no hystersis. So if the input voltage is close to 5 Volt, neither of the LEDs will glow. However you can add hystersis to your circuit by providing a feedback resistor from the output to the + input and series resistors as in my circuit. If you use the same resistor values, you will have about 60 mV of hystersis.
2. you need two supply voltages.
However, it has the advantage that there will be less current required since it does not have the 2 resistors in series across the supply that mine does.
As for your question about the about the positive or negative power supply's, I don't know which IC you intend to use, so I don't know what common mode range it has. In general, you would need supply voltages of at least 8 Volt.
If you make the resistor in series with the LEDs 1k, you will have a LED current of about 6 mA for supply voltages of +/- 8 Volt. If you want the LEDs brighter or dimmer, change the resistor to another value.
You should check the data sheet of the IC you use to ensure that it can source the LED current.