HID stands for High Intensity Discharge.
HID headlight bulbs put out many more lumens than OEM halogen bulbs. The housing that reflects these bulbs are either designed for halogen or not. A HID bulb in a halogen reflector would cause so much light scatter that it would make on comming traffic to think you had your high beams on +10.
Current HID bulbs are projected through HID projectors, which is a lens with a shield that makes a solid light cutoff line in a DOT specific shape. There are a few instances of HID reflectors like older Escalades that were designed for HID bulbs. There are many instances of halogen projectors as well, they look cool but are cheaper to make.
I would question any square shaped reflector made for HID bulbs. There may be too much light refraction to blind on comming traffic. HIDs put out so much light they must have a cutoff for low beam settings, which is a challenge for non projector style housings.
Color temperature, watts, and ballast style mean nothing compared to the manner in which the light will be dissipated on the road.