Capacitor vs battery which cost less per capacity?
I expect that the traditional Lead-Acid battery will be the best choice for this application at this moment.

Have a look here: allaboutbatteries.com
Scroll down a bit to the green table and notice that indeed Lead-Acid
batteries have the lowest Cost per stored WattHour.

In the coming years this might shift to Li-ion based batteries as these improve in cost and performance (there is less development in the Lead-Acid department I believe). Li-Ion batteries are more difficult to use than Lead-Acid batteries though. Lead-Acid batteries are more robust in general.