But I do know that my big battery (not GM) on my bike at home (which is 20 amp hr) cuts off at a much lower voltage.
Is your other battery LiFePO4 as well, and is the voltage lower when it is fully charged?
If the motor load
(Amps being drawn) is the same for both batteries, the bigger battery will also be under less load in relation to its output ability and will therefore have less voltage sag
(Drop in voltage) under load, so it should discharge more of its capacity before the Low Voltage Cut-off
(LVC) is activated which would also lower the voltage further.
If you were to use two 10Ah packs, one at a time until each pack was fully discharged you would not go quite as far as using both packs simultaneously
(connected in parallel). When both packs are supplying the required current, each pack
is only having to supply half of the required current instead of all of it. Reducing the load on the battery by 50% also reduces the voltage sag.
If you look at the following graph you can see quite clearly how much difference the load makes:
A 10Ah battery delivering 20Amps is discharging at 2C, but two 10Ah batteries in parallel delivering 20 Amps
(10Amps each) are being discharged at a rate of 1C.
If we assume that the LVC is activated when the cells reach 3V the batteries discharging at 1C would output around 85% of their capacity, whereas the single battery discharging at 2C would drop to 3V/cell much sooner, only delivering around 75% of its total capacity.
If the LVC was set at 2.8V/cell, according to the above graph, the 10Ah pack would deliver over 90% of its rated capacity
(10Ah) at 1C, but would only deliver around 50% of its capacity at 5C
(50Amps load).
I hope this makes sense.
Alan