Why is it that an LED bulb can not work inside a projector but a HID can?
Sorry for the long explanation, but I encourage to read it and understand it.
When manufacturer (or seller) says that his LED bulb is a "direct replacement" of halogen bulb they are simply lying to you. Not because they don't like you. No, this is because if they don't lie, they would not sell a single bulb. Some people have no clue about some LED bulb facts, so they believe and they buy it. After trying some buyers still believe in that lie and play along (or they are too dumb to understand the result).
The headlight (low beam) is designed with two goals: give the best light output to allow the driver to see, but at the same time do not blind the drivers from oncoming traffic or drivers on the same lane in cars just in front of you. And of course the lamp is designed strictly for the particular bulb to use.
The problem with LED bulbs comes from the geometrical difference between the source of the light. In halogen bulb the source of the light (filament) is placed precisely in the center of the bulb and it shines the same flux all the way around. The source of light in LED bulb (LED chip) sits flat on the mount and shines mostly in 60 degrees from the line perpendicular to the base. So one LED chip shines only 120 degrees comparing to 360 degrees in halogen bulb. To cover the back side most led bulbs use at least 2 LED chips with the second chip shining in opposite direction. That will cover 240 degrees, but still not full circle. That will create some dark spots in final lamp output.
Now the thing most buyers don't understand: because there are two LED chips separated by the base (heat sink) neither one can be in the center of the bulb - they are in offset by the thickness of the LED chip itself and half of the thickness of the base. In most bulbs it will be at least 1/16th of the inch. That is a lot for a lamp geometry. Because the source of the light is not where the lamp designer expected it to be, the output pattern is completely out of whack. The cut-off is lost, there are "ghosts" of light where the dark side should be, and dark spots on the lighted road.
There is no solution to that other than redesign the reflector (or projector) to accommodate the LED bulb as a light source. What is the worst of that, the high power LED bulbs with whiter light will appear to be brighter, and therefore they blind the other drivers even more.
I see it every day on my commute. I don't even bother "flashing" these guys. If they did not figure it out yet, they wouldn't understand my "flashing" either.
HID bulbs while they are not exactly perfect (not 100% same as halogen bulbs) at least the source of the light (arc) is centered (similar to halogen bulbs) and shines 360 degrees (same as halogen bulb). The arc is a bit longer than halogen bulb filament, so it creates some "ghosts", but if used in projector type lamps these ghosts are mostly eliminated. In reflector type lamp these ghosts are almost as bad as from LED bulbs.