HID will always be brighter then OEM halogen headlights. As said, there are 2 main types of headlights, reflector and projector. Both of which can be used for HID. Like the reflector headlight, projector type headlights also utilise a reflector which collects the light and directs it to the projector lense. This lense can better disperse the light in a uniform and controlled manner which is essential for HID as glare is a big problem on the road. Modern reflector headlights however have a series of reflectors which also produces a cut off line and kick-up but with some spill light and hot-spots on the road.
The throw of light also depends on the colour temperature. OEM Halogen bulbs are around 3000K-4000K, OEM HID is around 4300K, aftermarket HID kits are anything between 5000K-12000K. Generally speaking the lower the temperature colour the better the throw. Hence yellow streetlights/foglights, this is also part of the reason why incandescent torches have good throw.
The cut off shields are to provide a smooth "cut off" line and also for the "kick up" splays which inherently points towards the pavement side. On a bixenon HID setup, the high beam is activated by removing these shields.
The law governs both types of headlights. The throw can be adjusted by putting higher output halogen bulbs in but no halogen bulb will match the output of an OEM HID bulb. In the UK Halogen bulbs are approved by an "e-mark" this denotes conformity. HID bulbs are also regulated in this way.
But in answer to your original question, I am not sure why you say HID does not throw far. In my experience it throws much further than a Halogen setup.