The relationship between current, discharge time, and capacity for a lead acid battery is expressed by Peukert's law. The efficiency of a battery is different at different discharge rates. When discharging at low rate, the battery's energy is delivered more efficiently than at higher discharge rates.
In general, the higher the ampere-hour rating, the longer the battery will last for a certain load. Installing batteries with different A•h ratings will not affect the operation of a device rated for a specific voltage unless the load limits of the battery are exceeded. Theoretically, a battery would operate at its A•h rating, but realistically, high-drain loads, which can occur in digital cameras, can result in lower actual energy, most notably for alkaline batteries. For example, a battery rated at 1900 mA•h may not sustain a current of 1 A for the full two hours.