In short: Led is the most efficient, halogen is only a little better than your old-school lightbulb. In other words, horribly inefficient. I have never heard of dichroic lamps, but I am no native speaker. A short Google search resulted in the information that "most dichroic lamps are in fact halogen lamps".
Nowadays you should get every light technology in almost every base. LEDs sometimes come built-in in new lamps, because they have a very long lifetime. (over 10000 hours if I remember right).
I don't know for which purpose you want that information. If you want to modernize your home I would recommend using only leds. They are more expensive, but you never have to change them. And they are the most efficient solution on the market.
However, leds have drawbacks. You should get familiar with terms like color temperature, lumens and color quality . It is not as easy as buying a incandescent lamp. The above link claims not to be exhaustive. Just do a Google search for terms that you don't fully understand.