1: They are physically larger, to fit in devices that need the. 2: They may have a larger surface area in the "sandwich":, which means lower internal resistance, so it can produce more instantaneous current.
Apples and oranges The capacity of a battery is solely dependent on the weight (mass) of chemical reagents packed inside. The D size package is bigger than AA size, so it has greater capacity for both current draw and operational time, if both use the same formulation. Now if you were to compare a 25 cent cabon zinc D to a $8 silver oxide AA, then the AA wins because the chemicals used pack more energy density.
But the trade off is price. Not every one is willing to pay $32 for each battery change. But if you use an easily rechargeable battery of the nicad or NiMH class, then your AA size won't be able to compete with the CZ or alkaline D level of performace, per charge cycle.
With electronics becoming more efficient, there are fewer devices that need the oomph of a D size battery of any chemical formula. And the AA with its compact size and lighter weight becomes the new design standard. Even for flashlights, now that LED bulbs are available.
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