Steve, for your trips of 6 miles you really don't need a big battery.I have a question about batteries. You can get a 13AH or a 15AH. I see the 15AH will get you further. I am interested in whether the 15AH also gives you extra pedal assist for the steep hills? That is, does it only increase the number om miles, or does it also give you some extra oomph?
Batteries that last the longest are the ones that are used the most. It is likely a larger battery that is hardly ever depleted will not last as many years as a smaller battery that is regularly given a good workout. I recommend you go for the smaller battery option.
Both will maintain around 38-40 volts for that length of journey even on Sheffield hills.