Generally speaking, a manual transmission will be more efficient. That's assuming you know how to drive it efficiently.
However, the automatic transmission has undergone a paradigm shift. Many of the automatic transmissions nowadays are automated manual gearboxes, or CVTs. And the fuel economy can rival or even beat a manual transmission, depending on how you drive it.
So the answer to your question would depend on which particular transmissions you're comparing, and your driving habits.
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