An important reason to choose the charging method is the chemistry of the rechargable battery.
Lead acid batteries need constant voltage charging, Nickel Cadmium and Nickel Metal Hydride need constant current charging ( and that these currents MUST be reduced as soon as the batteries reach full voltage )
Lithium Ion batteries - I can't remember off hand if it is CV or CI charging but great care must be taken to avoid overcharging or deep discharging as permanent damage will be caused in either case.
Here is another useful website
http://www.batteryuniversity.com/