Battery

The easy way to figure out how much power any given setup will give you is to look at the watts.  Volts times amps = watts.  Another way to restate what David said is, when you parallel batteries the voltage stays the same but the amps are added.  When you series batteries the voltage is added but the amps stay the same.

Two batteries of the same size, one 6 volts, one 12 volts, will have roughly the same wattage available.  The 12 volt battery might be rated at 110 amps for your average battery (20 hour rating, a standard measure for deep cycle batteries... another discussion for another time), the 6 volt battery at 220 amps.  The 12 volt battery has 6 cells @ 2 volts each, the 6 volt battery has 3 cells @ 2 volts each but they are twice as big, which is why the 6 volt battery has twice the amperage.  Either way, you get 1320 watts.  Really half that since you shouldn't discharge a battery more than 50% most of the time.

Wattage is a portable number over different voltages (as you can see above), so its a useful number when calculating loads, too.  Especially when you are using an inverter.  So a 100 watt load at 120 volts is still a 100 watt load at 12 volts (plus the overhead of the inverter itself).  The difference is the amps.  At 120 volts you are using .83 amps, but at 12 volts it is 8.3 amps (plus overhead).