The size of a battery cell determines how much stuff is inside which determines how long it can supply a certain amount of current.
Two AAA alkaline cells can supply 25mA for 40 hours when the voltage has dropped to 2.0V.
Two alkaline button cells can provide 25mA for a couple of minutes or less when the voltage has dropped to 2.0V.
If size isn't an issue for really low current drain applications think Lithium. Not the common Li-poly cells that are in everything now days, but Lithium primary cells. The have really low self discharge rates, and extreme shelf life, 10 years or better under discharge or not for backup applications. Still able to supply current up until it's end of life for short duration.
In general, for a particular battery chemistry, (alkaline, lithium, etc.) the larger the battery, the lower the cost per watt hour of energy. So it's generally a trade-off between the cost of battery operation and the room you have for a battery. For alkalines, the AA size seems to be a good compromise for many electronic applications.
Lithium primaries comes in 1.5volt output in a AA form factor, they're much more expensive than alkalines but for backup applications where size isn't an issue they're king.