Dear Joseph,

I think one of the possible answers is in your own question you asked in the last, what to compare ?

You should keep on comparing input voltage (6volts) with the regulator output voltage(5volts), and as long as the two voltages are not equal it should not trigger the warning for low battery.

Take the regulator output 5v as reference voltage for comparator.(Vref.)

Take the direct battery output 6v as the input to comparator.(Vin)

Use the comparator out put as follows:

Not to give warning when (Vref. < Vin)

Give warning when (Vref. = Vin)

Hope it is of any use

Good luck

Babar/