I am buying a tool that has two options to power - rechargeable battery or dry cell. Personally I prefer rechargeable battery but it is not a tool that will be used so often - probably only used once every year. Does a rechargeable battery that is seldom charged and discharged last much longer than one that is charged and discharged daily? Or will it just degrade at more or less the same speed no matter what?

To get the Anode and cathode activ it needs charging and discharging. No use will get residius on the electrodes. Strong use charging and discharging also minimize the lifetime by dissolving of the electrodes. The longest lifetime is achieved to have small discharging and charging current.  For this you can buy small rectifier to do this job, voltage controlled.