Generally speaking the drivers most people start modding with can be divided into two groups.
First there are regulated drivers like the Qlite. These keep the current limited until the point is reached that the voltage of the battery sags below the forward voltage of the led. A high drain battery is better able to keep up a high voltage before sagging.
FET drivers are also commonly used. They act as an electronic switch. When open, the full power of the battery goes to the led. It is quite possible that the current is higher than (parts of) the led can handle. Especially if you did your best to eliminate all possible resistance in the flow of the current. Like bypassing of the tailswitch and driver spring.