If I have two batteries with the same voltage (say 8V) and one has 1000mAH and the other is 2000mAH I would expect the 2nd to last roughly twice as long as the first given the same usage. But given one 8V 1000mAH battery and one 11V 1000mAH battery, and the voltage range of a Fez device (6-12V)… Will the 11V battery last longer because less energy is used or is the extra voltage wasted and they will last about the same amount of time?
You will just waste the extra volts into heat. You may even damage your board regulator since over 9v it will fry. If you need to use a 11v battery, just use a DC-DC converter such as those http://www.robotshop.com/ca/Dimension-Engineering-AnyVolt-Micro.html (depending on what power you need). They will waste a little power in the conversion, but much less than the usual regulators than just convert the extra volts into heat… 8)
The best would definitly to find a 6 or 7V battery with as much capacity as you can get… that will last the longer !
Since the battery voltage is far to be constant, you may wish to use a DC-DC converter anyway to make sure to get a constant output voltage to your fez, whatever you battery is delivering.
Great information about Li-Ion & LiPoly batteries here : http://www.ladyada.net/learn/lipoly/
Fellow Aussie Dave Jones had a good battery capacity video blog a while ago, more info than you’ll need but interesting none the less: http://www.eevblog.com/2011/01/23/eevblog-140-battery-capacity-tutorial/