The basic, conventional and the easiest way to supply a LED is constant current. However, it must be low efficiency, especially when you need to adjust its brightness for any specific purpose, or you have to supply LED from wide range of source voltages. At those cases, PWM is the better solution.
For both of circumtances, you can get the same brightness if you give the LED the appropriate currents/duty cycle.
Just "google" on internet, tons of PWM applications of LED over there.
nguyennam