If you wire 2, of the same 12 volt batteries in parallel, you will effectively double your Amp hours while retaining 12 volts. So really the answer to both questions is the same, you increase your available amp hours, which automatically means you can go longer between charges.
If you wire 2, of the same 6 volt batteries in series (required to get up to 12 volts) your amp hours will not increase, but the 6 volt batteries have impressive amounts of storage compared to the 12 volt versions. So the goal in that case is to make a 12 volt system out of 2, 6 volt sources. Wiring in series does that.
More info, easy to understand-
http://www.trojanbattery.com/Tech-Su...nsDiagram.aspx