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No one claimed that deep cycle batteries last longer. The difference is that with a acid base battery, the acid no longer carries a charge in an effective manner once the battery is completely discharged. A chemical reaction takes place as the battery discharges, rendering it almost useless. More specifically, it's the acid interacting with the led core. Once the reaction is completed, the battery no longer holds a charge. It's irreversible. High school chemistry.
A gel-cell, deep cycle battery, can be depleted and recharged numerous times without losing it's ability to hold a charge. It can be cycled (charged/discharged) to a much greater degree (hence the "deep") without any ill effect on the batteries performance.
In regards to lifespan... I have yet to see a major difference in duration/lifespan if both are cared for properly, and not strained (i.e. underdrive acc. pulley, huge sound-system, leaving the lights on..etc...). If someone tells you otherwise... let me know as I'd like to see the proof.
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