When you say flat screen, do you mean thin-profile sets?
Most of the DLP sets are rear-projection sets that have considerable depth to the cabinet (InFocus makes 50-60" DLP sets for themselves and for the RCA brand that is only 7" deep, but this is generally the exception).
As a rule, Plasmas and the thin (backlit, not rear projection) LCD sets have the advantage of being brighter than any of the rear projection sets). Plasmas also have reasonably good color. The principle objects I have to Plasmas are that: (1) they cannot be viewed at close distances (somewhat reducing the big screen experience) because the pixel structure is clearly visible and because other artifacts (e.g., mosquito noise) are particularly bothersome with plasmas; (2) they are prone to burn-in problems (should not be viewed with a border around the picture for great lengths of time meaning that non-widescreen material will have to be blown up into a picture that is slightly distorted in shape); and they can produce a lot of heat (particularly 50"+ sets). I like Panasonic plasmas, particularly considering the price, but, to me, the Fujitsus are still the best because their processing creates a picture with less visible noise and other artifacts.
Backlit LCD sets are bright and punchy looking, have a less obvious pixel structure than plasmas and are not subject to burn-in problems. But, the inability to respond quickly to changing scenes creates all sorts of weird motion artifacts. I also don't like the cartoon-like homogeneity of images that should have subtle differences in color and texture (plasma is better in this respect). Also, some of the larger LCDs with more than one light source develop uneven lighting problems as the sets age.
The thin DLP sets I've seen were surprisingly good, considering that I expected problems with edge focus from having to somehow project at an extreme angle. The sets looked like regular rear projection DLP sets. That means they also had problems typical to rear projection DLPs. First, the picture does not look as punchy and vibrant as a plasma or backlit LCD set, particularly if there is a lot of ambient light in the room. Some viewers (like myself) see rainbows (color separation) and some even suffer from eye strain when viewing DLPs (I don't). In large patches of color or white areas, the screen will exhibit tiny sparkling grains (caused by the interaction of the fixed pixel structure with the lenticular projection screen). The big pluses for DLP is that it does not suffer as much from motion artifacts, does not suffer from burn-in, and the picture should not significantly degrade over time (the bulb can be replaces, one cannot reverse the aging of pixels in a plasma).
Currently, some pretty good LCOS/SXRD sets are coming on the market. These sets use reflective chips, like the DLP sets, but typically use three chips so they do not cause eye strain or have any problems with visible rainbows. The downside is primarily cost and the fact that thin-profile sets are not available. I own a Sony Qualia set. I think it delivers the best rear-projection picture currently available, but, it is very costly. Sony is now delivering a much lower cost "Wega" version, using its SXRD chips, that seems to have just about all of the features of the Qualia set (except, slightly small screen size and lower power bulb). I bet this is a real winner.
The latest technology that is expected to be available starting late next year is SED. This type of set is like a plasma and uses phosphors to emit light, like a plasma, so burn-in might be an issue. But, the word is that this technology is capable of delivering black levels like only old CRT television sets are currently capable of delivering, and has a quick response like old time sets. In short, this technology promises to bring the superior picture quality of old-time CRT televisions to a much larger screen size, and, with a profile at least as thin as plasma sets.
