There are essentially two types of HD projector.  There is the liquid crystal display or LCD HD projector and the DLP HD projector.  The original HD projectors were all of the LCD type and generally were considered perfectly satisfactory.

However, a number of years ago a company called Texas Instruments designed a new type of projector, the DLP HD projector.  Generally speaking the DLP HD projector is more expensive than the LCD HD projector but the significant advantage of the DLP over the LCD is that the design of the DLP allows the casing in which the projector is housed is smaller, more compact and lighter which makes the DLP projector the more portable of the two.

Overall the DLP has slightly worse color quality but slightly better picture quality than the LCD projector.