Billson,
For the Badboy, the converter will try to generate a higher voltage than the input and it will do so until it gets to the current as defined by the sense resistors installed. When the converter senses the current to the load has been achieved it throttles back on the "gas" pedal so to say. Otherwise, it has a lead foot and stomps on the gas.
The downboy does exactly the same thing, with the exception it is trying to put out less voltage on the output. The downboy steps or converts the input voltage to a lower output voltage. This is called a step down (buck) regulator. It too will try the put out power until the output current is achieved. Since the Downboy is wired differently, it does not have run away condition like the Badboy does.
The reason both could be confusing is they both will work on the 1W or the 5W and like others have explained above the output LED sets the output voltage (Vf of the LED). The Vf output voltage is the mid point. If you battery voltage is above Vf, you need to step down (Downboy) and if your battery voltage is below Vf then you will need to step up.
For the 1W/3W the midpoint is appoximately 3V-4V depending on the Vf bin code of the LED.
For the 5W, the midpoint is twice that or around 6.2V-7.8V.
So, a 2X123 voltage is 6V which is higher than the 1W/3W Luxeon yet lower than the 5W Luxeon.
The two key factors are Battery voltage (fresh and near dead) and the Vf of the LED.
With these two you should now be able to determine if you need to step up the battery voltage to the output Vf voltage or step down the battery voltage to the Vf of the LED.