Budget make a difference.
I have a DLP projector (Boxlight Raven) http://xbox.boxlight.com/
I used to have an Infocus X2
Both are comparable to the Infocus 4805.
LCD projectors typically have the same problems as LCD monitors... and DLP projectors typically have the same problems as DLP RPTVs.
Referring to the sub $1500 projectors in LCD and DLP:
LCDs are typically washed out with not-so-good black levels, some have ghosting but that's getting much better. Also there is often a "screen door" effect because the pixels are spaced out too much. but you can get full 720p resolution out of a budget LCD projector, which is great. LCD is also an analog technology so even if the signal going in is digital it gets converted to analog before being displayed.
DLPs typically have lower resolutions (EDTV as opposed to HDTV, much like low end plasmas). They have much better black levels (particularly with the new "Dark Chip 3" tech) and much less of a screen door effect. No ghosting what-so-ever as the technology is actually magnitudes faster then other display types (meaning they measure refresh in nano seconds as opposed to micro seconds). "Single Chip" DLPs typically have "rainbow effect" problems that 10% of people can see. Which is when you see the colors on the screen separate when your eyes dart across the screen. so if there is a white line down the center of a black screen and your eyes dart from left to right you'll see the white bar separate for a split second into Red Green and Blue. Some projectors are better then others and most people can't even see them trying. If you can see them getting a DLP with a better color wheel (read more segments and faster speed). DLP is also the only true digital display technology so if your source is HDMI or DVI then you can rest assured that the signal is totally digital right up through hitting your screen.
I really like Infocus' products, they use top notch internal components like the Faroudja Scaler which is known to be the best scaler chip you can put in a projector. Basically you get the best quality for your money with them, which is why I like them.
If I were buying a new projector today I'd go with either:
Infocus Screenplay 5000 - LCD projector, true 720p resolution, no ghosting, DVI with HDCP, only down side is black levels aren't so spectacular
Infocus 4805 - DLP projector, Vibrant colors, great black level, DVI with HDCP, only down side is that it only supports up to 480p (720p and 1080i are both down scaled to 480p).
The Infocus X3 is really nice too.
No matter what projector you choose, expect to play in a completely dark room as the picture sucks otherwise. There are specialized screens needed to play in a lit room (like the coveted Sony Black Screen) and those can cost as much as one of these low end projectors.