Either works - but it is easier to deliver more energy to a device with a higher voltage. The reason for this is because as the amount of current increases through a wire, you lose more energy through heat. When running 6 volts, you need twice as much current to deliver X amount of watts as you would if you were using 12 volts. If you look at a 6 volt battery cable, you'll generally find the cable to be thicker - and with heavier post clamps. Six volt systems are less forgiving if you have any loose connections or worn connections.
And as mentioned by others here, using 12 volt systems are just cheaper and easier to maintain in most cases now. This is due to availability. As a side note here, I keep hearing that the major auto manufacturers will be switching to 36 volts "real soon now". Their reason: Newer cars demand more from electrical systems than ever. I can't wait - I have shelves of 12 volt communications radios and law enforcement electronics. *sigh*
Your six volt system will work, just keep everything well maintained.