Firstly, Cree is a manufacturer, not a model of LED. Cree makes a lot of different LEDs, and throw will differ widely between models. Worst throw will come from the MC-E and XM-L models, with the XP-G being somewhat better, the XP-E somewhat better than that again, and the XR-E having the best throw. This is due to surface brightness - the higher the brightness per surface area unit, the more throw you will get. Usually, smaller LEDs will have the highest surface brightness. Their size also makes it easier to focus their output.
As for HID vs LED, usually, HID beats LEDs in the throw category. This is because of the above mentioned fact. An electric arc will usually be much smaller than an LED (thus much higher surface brightness at the same output level), and in a proper HID light situated right at the focal point of the light's reflector, giving it great focus.
Another factor, which is arguably more important, is quality and reliability. An LED light in the price class you mentioned will be a good quality light and will probably last you a lifetime. However, $100-150 for an HID light is another story. If you buy an HID at this price point, it will probably disappoint you, and maybe even fail you altogether sooner than you'd like.
Problems with HID lights with 'LED price tags':
- very long warmup time. We're talking a minute or more for the worst offenders. Compared to the instant-on of an LED, this is a big drawback.
- long wait between restrikes. You can't just turn it on and off like an LED light. This counts against the lights practicality in actual use.
- poor quality and Q/C, especially the no-name brand ones so common in this category. Failed ballasts and/or lamps are common.
- poor build quality, usually cheap ABS plastic housings for the 'megamart' type store chain lights.
Basically, my personal recommendation is to buy an LED light regardless of the HID's theoretical superior throw, unless you are willing to spend a lot more on an HID. Output and throw aren't the only things you should consider when buying a light.