Its my understanding (please don't beat me) that if the chemistry is the same, and the size of the battery is the same (deep-cycle only, not car starter batteries), a 6-volt battery will have plates that are twice as thick as a 12-volt battery.
I believe the problem it addresses is that when a battery is deep cycled and then re-charged, some of the battery plate erodes.
A car starter battery is only discharged for a few seconds to start the engine, then the alternator immediately re-charges it, and the alternator also then powers the electrical load of the engine and car as its running. As a result, it can have many paper-thin plates connected in series-sets to get 12 volts, then as many sets as can fit, are connected in parallel to get as many amps as possible for a given case size.
Golf cart and RE batteries are often deeply discharged, and I have been told the plates can be as thick as a finger to help them last longer (anyone know for sure?).
If I'm right, and you only need 12 volts, 2 of the 6-volt batteries in series will have half the plate surface area compared to 2 of the 12-volt batteries in parallel. The two 12-volt batteries will have twice the amp/hours, but if the size of the two 6-volts have enough amp/hours to do the job, they will last twice as long.
I think a more useful comparison might be: to get 48 volts (from batteries that are the same size and price), you can use 8 of the 6-volts, or 4 of the 12-volts. In this example, the pack that costs twice as much will last twice as long. If you can't afford the big pack right now, you may need to get the smaller pack and replace them twice as often.
Another important consideration is that extra deep cycling can lead to an early death. If you sized the battery pack large enough so that you only use 1/3 of its capacity before it is recharged, instead of 2/3rds, it SEEMS like only using half as much, it would last twice as long. However, I keep reading that buying twice the amp/hours will make it last 4 times as long. Its something about during charging there is electrical flow that is reversing the sulfated portions of the plates, but the un-sulfated portions are also experiencing electrical flow leading to ionization and erosion.
Don't spend a lot of money on anything I say, I'm still learning...