The following is from a GE website
http://pressroom.gelighting.com/facts/cfl-vs-halogen-vs-led-232394 While it is aimed at indoor lighting is still valid for comparing automotive lighting. CFLs are compact fluorescent indoor bulbs that are all the rage today.
Halogen
Halogen bulbs have a tungsten filament just like incandescent bulbs, but halogen bulbs also are
filled with halogen gas. When the bulb is lit, tungsten from the filament is evaporated into the
bulb’s gas, providing illumination. The halogen gas then carries the evaporated tungsten particles
back to the filament and re-deposits them. This creates lower energy use for the bulb.
Best Applications
High-intensity reading lamps, office lamps and display lighting where users want to spotlight
artwork or photos and outdoor applications where bright light is needed.
Key Features
Many are 10-20 percent more energy efficient than incandescent bulbs.
Instant start. Halogens do not experience the delayed warm-up associated with CFLs.
Fully dimmable.
Produces a bright, crisp light.
LED
LEDs are small light sources or thin chips that become illuminated by the movement of electrons through a semiconductor material.
Best Applications
Outdoor lighting where fixtures are left on for extended periods and changing bulbs is not easily done. LEDs also are fitting in linear applications, such as under cabinet lighting, where bulbs/light sources with thin profiles are needed.
Key Features
LEDs can use up to 75 percent less energy than incandescents.
Lasts up to 25 times longer than incandescent and halogen light sources, and up to three times longer than most CFLs.
Instant start. LEDs do not experience the delayed warm-up associated with CFL bulbs.
Small LED chips allow for more compact, design-forward fixtures, as well as the illumination in tight areas.
Cooler to the touch.
Robust … no filament to break.
Most emit light in a specific direction, versus in all directions, but GE’s traditionally shaped LED bulbs are omnidirectional. That is, they are designed to emit light all around, just like a standard incandescent light bulb.
The above is assumed to be a comparison on equal light output. For automotive applications halogen bulbs generally put out more light (lumens) then the incandescents they replace. That is the reason most use halogen lights.
There are plenty more sites to compare different lamp options.