I think we're addressing two different aspects of this...
The voltage of a battery changes. You can measure 4.2v at the battery w/o load but that drops as amperage increases. It also drops as you drain it. Even if it is the same energy expended from this chemical conversion.
If a 1A load is put on a battery I will get x mA out of it until it drops to a per-determined voltage. If a .5A load is put on it the total mA I get out of it will be more and over a longer period of time. As far as I know this is true of any type of Li-Ion and I think NiCad also. See
HERE for actual measurements.
The original thing I was addressing was "
Why is it easier on the batteries to draw lower amperage". What I failed to address was that part of the indirect question was that there was a device here being used to adjust the load on the batteries and I think that is your point.
In this case the device is the load not the atty. The device can be adjusted to draw 4A or 3A or 2A from the batteries. All aspects of the battery chemistry will be 'better' at the 2A draw and the voltage will be higher and remain higher for a longer period of time. Which I thought was the original question... maybe not.