The PJCCS, unlike the original C4S, adjusts its current according to the available voltage. I made this change because ordinary alkaline batteries will lose voltage over their life, and I wanted the Quickie to run well even when the battery drops to 2/3 of nominal. It should work fine at higher voltages as well.
(The other change is that it is not a cascode, and does not have as high an effective impedance as the C4S. The main function of extremely high impedance is to improve the power supply noise rejection, which is of course not so important with a battery. The reason is that less compliance (voltage drop) is required, so it works better with a low voltage supply.)