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@grams
Batteries usually have faster discharge curves under heavier load, i.e. the faster you try to extract energy from a battery, the less total energy you get out*.
Assuming the 4Ah battery is just twice as many of the same cells in parallel as the 2AH, each cell is carrying half as much load, and because of the above will last more than twice as long.
OTOH having two batteries will let you continue working while the other battery is charging which can give you something resembling infinite battery life, so do that.
(* The "2Ah" rating itself is based on applying a particular sized load, as you'll get a different number depending on your test current)