The newer Liquivision computers take a somewhat odd size of battery that has evolved a bit from the original. The early batteries that fit into the black battery holder were a smaller form factor and had less capacity. The current form factor is basically 17335 for primary cells or 16340 for rechargables. However not all 16340 batteries are the same length. Those with internal protection PCBs are too long to fit in the white holder. This also rules out any CR123 or RCR123 batteries, which is somewhat unfortunate, as they can be easily purchased in many stores.
The advantage to the blue primary cells (17335) is their long shelf life. I keep a couple with me in case my rechargables fail. I currently have two sets of IMR 16340 cells, keeping one set charged while the other set power my Kaon and Xen computers. The advantage of the IMR cells is that they use a safe chemistry and don't require the protection PCB. While their rated capacity (550 mAh) is somewhat less than other rechargables, their lower internal impedance and high current capability give them a more stable operating voltage while in use. They come out of the charger at about 4.2 Volts, and I recharge them when they reach 3.7 V. My computer is configured for the green cells, and I have it display the voltage for battery status.