The charging amps or the load amps.
What ghurd said.
In series strings each battery in the string has to deliver the full amps delivered by the string. In parallel strings each battery has to deliver the amps delivered by the string divided by the number of batteries in the string.
If you're connecting four 6 volt batteries in series for 24 volt, if the string delivers 100 amps to the inverter (2,400 watts of DC power), then every battery in the string has to deliver 100 amps.
If you're connecting two 6 volts in series for 12 volt, then paralleling the two 12 volt strings for 12 volt output to the inverter, then you're looking at 200 amps of output (2,400 watts of DC power). Each series string will deliver 100 amps, and each battery in the bank is still delivering the same 100 amps.
With the 24 volt configuration, 6 AWG is OK for the interconnects but you'll want 4 AWG or bigger to the main DC bus or disconnect because the run will be longer.
With the 12 volt configuration, 6 AWG is OK for the series wires but I'd use dual 4 AWG (a positive and negative from each series string) to the main DC bus or disconnect up to 10 feet away. I would not parallel the two strings, then pull off one end of the parallel wires. Use the bus to do the paralleling of the strings.
With stranded battery cables, you can use the following guidelines for a run of 10 feet and a voltage drop of .5 volt.
6 AWG is good for 82 amps or 853 watts
4 AWG is good for 131 amps or 1,355 watts
2 AWG is good for 208 amps or 2,151 watts
1/0 is good for 330 amps or 3,414 watts of DC load
It's nice to have series and parallel wires all the same length, but if you're dealing with lengths under 1-2 feet it don't make much difference.
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Chris