We stand by our answers -- yes, you may use AAA, AA, C, or D cells interchangeably, as long as they are wired up the same way and that you can make them fit.
The big difference between these batteries, apart from size, is really the total energy stored in them. Adam said the current was different, but as you correctly note, it is not the battery (usually) which determines the current which flows, it is the load. A battery pushes electrons in wires with a voltage that is fixed at 1.5 volts (if you're using one of the batteries mentioned above, and it's not dead or shorted out). Then the load determines how much current will flow, often obeying Ohm's Law, V=IR, or whatever the load requires at the voltage it's being driven at. Only if the load requires lots and lots of current will the voltage on the battery sag below its rated voltage (or if the battery is wearing out). (I believe that the maximum current that can be supplied before the voltage starts to sag does depend on battery size. So a small battery might fail to work in some applications even in the short run./mbw)
So then the difference between the battery sizes isn't voltage, and it isn't current (except under extreme circumstances where the battery is shorted out). It's the product of current*time, which is proportional to the total energy stored. Run a piece of equipment with bigger batteries which have the same voltage, and you'll have to replace them less frequently.
I'm not sure what you mean by "efficiency". All sorts of batteries are very efficent at low current draws. The only loss I can think of when oversizing a battery for a particular application is that its "shelf life" will expire while it is sitting in a device which uses up much less energy than is available. Then you'd still have to replace the battery after its lifetime, regardless of whether a smaller battery could have done the same job in the same time. This is normally of minor concern, as you'd have to change the batteries at a minimum of the shelf-life of the battery anyway, and then it's just a case of spending more money on big batteries versus small ones (battery price doesn't always scale with battery size, though). What is perhaps more important is the inconveniece of lugging around those big, heavy batteries if they're not going to be fully used by the time they get so old they stop working anyway.
(published on 10/22/2007)