Brightness or burn time
Brightness and burn time are two inextricably linked parameters of any headlamp, regardless of its lighting technology. For a given quantity of energy, increasing the brightness automatically decreases burn time, and vice versa.
For a compact headlamp worn entirely on the head, the energy source (standard or rechargeable battery) has a limited capacity in order to reduce size and weight for the sake of comfort. In spite of the improved performance of today's LEDs and batteries, this still limits the capacity of a headlamp to provide both significant brightness and long burn time.
the shape of the beam directly affects lighting distance
Lighting distance depends directly on lighting power, but mainly on the shape of the beam.
In fact, given the same light output, lighting distance will differ depending on the shape of the beam. For example, 100 lumens of light will project to 40 meters with a very wide beam, but up to 100 meters with a narrow beam.