There is no inherent advantage of six volt pairs over 12 volt provided both are apples or oranges.
The difference comes in when you have six volt apples and 12 volt lemons.
Here is what I mean
Though you can find 12 volt DEEP CYCLE batteries, the tend to be either smaller (Like 5 or 20 amp hours) or much bigger (Group 31 to some truly giant jobs used in Fork Lifts).. They also tend to be EXPENSIVE!!!!!
The most common six volt battery is a True Deep Cycle, (Designed for use in Golf Cars) and due to the popularity of golf cars one of the least expensive, if not THE LEAST expensive, lead acid battery made.
Thus. I recommend them. Most bang for your buck and it is that simple.
Still. Lots of folks here are in love with very high priced AGM's and such and sing their praises.. I tried 'em. Never again.,