You need to match the load to the battery. If the watts out (current times voltage) is the same, the power output is the same. The big problem here is minimizing the IR losses in the wireing between the load and source, the higher the current the bigger percentage of the available power is lost in the transmission of the power.
I see that some are still under the impression that NiCad has a memory in the way we are using them here, not true. Now both NiCad and NiMh do have the problem with voltage depression (note NiMh is not immune from this same problem) which many mistake for memory. This myth about memory has been around for several decades based on the erroneous interpretation of the results of some of the early satellite problems and just won't die no matter hard or complete the chemist's and physicist's explanations are.