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The major advantage of two 6 volt batteries versus two 12 volt batteries is efficiency:
Two 6 volt batteries wired in series ensures the pair will always operate in tandem, which is to say the current flowing through the two batteries is equal. Any impairments affecting current flow (corrosion, resistance, etc.) affect both batteries equally.
In the case of two 12 volt batteries wired in parallel the current in theory is divided between the two batteries equally. The problem arises that theory does not match reality with a pair of 12 volt batteries and due to battery dynamics and differences in resistances between the two paths (often caused by corrosion, wire length, or resistance caused by quality of the connection) one battery will work harder than the other. The two 12 volt battery configuration can result in shorter battery life as the harder working battery ages faster.
The issues in using a pair of 12 volt batteries can be minimized by ensuring good quality connections, matched wire lengths (+ to + and - to -), and keep terminals clean.
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