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At the same 48V battery voltage the controller will deliver the same power to the motor that it always has since Power(P) = Voltage(V) x Current (I). The controller is limited to a max current (I) of 15A by design. The battery voltage is fixed at 48V. Thus the max power to the motor is the same with either battery regardless of battery capacity.
You can think of voltage as being analogous to water pressure in a pipe and water flow itself as being electrical current. Higher pressure (voltage) will push more water flow (electrical current) through the pipe. If the pressure (voltage) doesn't change the flow (current) will stay the same regardless of where the pressure (voltage) comes from.
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