It would be remiss of me not to mention the difference between how LEDs and Halogen bulbs work at the outset, since many advantages and disadvantages of each lighting system, is tied directly to how they work. In fact while this post ultimately compares CG Automotive's LED bulb kit, with my OEM Halogen bulbs, you will find that the difference in processes and the choices made for the particular Bulb kit, imposed by the processes, drives the comparison. Lets dive in. Regarding the LEDs process, I can do no better than Phillips' explanation that:

as indicated by its name, [light-emitting diode], the LED is a diode that emits light. A diode is a device that allows current to flow in only one direction. Almost any two conductive materials will form a diode when placed in contact with each other. When electricity is passed through the diode the atoms in one material (within the semiconductor chip) are excited to a higher energy level. The atoms in that first material have too much energy and need to release that energy. The energy is then released as the atoms shed electrons to the other material within the chip. During this energy release light is created. The color of the light from the LED is a function of the ingredients (materials) and recipes (processes) that make up the chip.

Compare this to a Halogen bulb's incandescence process.