Although graphene supercapacitors outperform lead-acid based batteries, this technology is not ready for the market. Then, in terms of solar energy harvesting systems the options are not a lot nowadays, without great improvements since the discovery of lead acid batteries 150 years ago.
Deep cycle batteries have better resistance to provide a great amount of current during large periods of time, while conventional lead acid batteries are better suited to areas where considerable discharging is not necessary and the goal is having considerable current in less time.
However, deep cycle batteries are sometimes more delicate and the user should take care of installing efficient current / charge controllers to keep the battery in optimal conditions during the long years of use.
For solar systems, the most used batteries are deep cycle, AGM and Gel, all lead acid based. The number or recharging cycles could be near 2100 or more retaining 80% of the capacity, nevertheless breaking the cost efficiency.