I think that some are confusing the issues. You can have HID headlights that use reflectors OR projectors. You can have projectors that have HID OR halogen lamps. For instance, our trucks have reflectors and halogens. A 1998 BMW 740iL has projector headlights but they use halogen (H1) bulbs standard. However the 750iL of the same year (or a 740iL of the same year with the HID option) has projectors but they have D2S HID bulbs and the projectors are slightly different.
Generally speaking -- on most cars you'll find that if they have projectors, they'll often have HID's because projectors originally were the best way to control the light and to make a sharp horizontal cutoff to keep from blinding oncoming traffic. The cost of making projectors is more than reflectors so they've started making HID's using reflectors. But you'll find that the HID's with projectors will have that flashy deep blue color that varies between bright white and blue depending on the angle of the light to your eye. This is because of the sharp horizontal cutoff of the light within the projector.
The reflector HID's seem to just dissipate the light more evenly and look like regular soft halogen headlights but are super white. They don't seem to provide that deep blue flicker that you can get with projectors. This is why many people who get HID upgrades to their plain reflector headlights are disappointed because they don't produce the blue reflection they want. So the aftermarket kits now have custom heat range bulbs that will emulate the projector look. IMHO it's still not the same tho as good projectors with HID's.
I hope this made sense.