In a ideal viewing room projectors can have superior picture quality to flatscreens. Projectors have higher pixel fill factor than flat screens (the gap between individual pixels that forms a grid pattern) so viewing distance to screen width ratio can be alot less, typical viewing distance is 1.5x screen width (not diagonal) with some people prefering upto 2x and others as close as 1x. The image is bigger occupies more of you field of view, this effects how your eyes track motion and results in less motion blurring and better immersion - illusion of being there. Depth cues in images are also better interpreted by the brain with a larger image, so the image can appear to have more depth, look more real. In a light controlled room real world sequencial contrast can be higher as the image is the only source of light in the room, in a dark coloured room real world simultaneous contrast can also be higher due to no glass screen causing glare/haze/reflections. Most projectors have seperate red, green, blue controls for bias and gain so the greyscale can be calibrated more accurately to D65 for a more life like colour image than many flatscreens that just have warm, standard, cool settings for greyscale. In a dedicated room the room is black and the image the only source of light, so your eyes are not colour biased by the decour or the type of room lighting, this also improves perceived colour accuracy.
Contrast ratio and gamma tracking are the most important factors for image quality. Greyscale colour accuracy is also vital.
On a greyscale ramp step pattern of say 5% steps, gamma is what determines the brightness difference of each step. It creates the perception of contrast, image depth, the 3D like effect. The higher the gamma the bigger the steps at the top bright end of the greyscale ramp and the smaller the steps at the bottom end of the greyscale ramp. Higher gamma = more contrast in bright images, less contrast in dark images. Since the three colors RGB used to make up the image are also tracking gamma, higher gamma = more saturated colour in bright images (the lowest - least bright colour in the mix determines how much white is in the mix as R+G+B=White), higher gamma will also shift the hue of the colour mix slightly towards the colour brightest in the mix (the ratio between the two remaining colours determines the hue). The reverse effects are caused by lower gamma.
Video is mastered on monitors using 2.2 gamma and is checked for robustness, it is expected to be displayed by consumers using up to 2.5gamma. Using gamma higher than 2.5 may cause problems with colour saturation with some sources.
The contrast you perceive is determined not only by the displays contrast but also your viewing conditions. The dimmer the display the less you perceive contrast, the darker your surroundings the less you perceive contrast. So for a projector which is relatively dim compared to a crt or flat pannel and is being viewed in relatively dark environment compared to a lit living room. You want to use high gamma as it increases the contrast in bright parts of the image. So I would want a projector that can do 2.35 or ideally 2.5 gamma.
For comparison 2.6 gamma is used by dci commercial digital cinema but with a different gamma curve than consumer video like dvds, blu-ray, etc... As commercial cinema uses a lazy s-curve. Film print projectors also use a lazy s-curve with an avearage gamma of 2.6 but the important middle part is a gamma of 3.0.
When checking out projectors have a look in the manual, usually available as a pdf on the manufactures website. They should list gamma presets. Sometimes these actually have numbers like
2.2(the reference crt used by the colourist)
2.35(the gamma used by European PAL reference crt colourists)
2.5 (the gamma for consumer crt according to America and the one you probably want to use in a home theater)
Sometimes they will give names like
Presentation (lower than 2.2, designed to be brighter so the presentation can use ambient lighting to enable people to take notes)
Sports (lower than 2.2, so people can see each other and the beer)
Standard (lower than 2.2 as expected to be used for daytime tv viewing with some ambient light)
Theater (2.2 to match the colorists reference crt, expected to be used in home theater with no ambient lighting but in practice too low for home cinema)
CRT (2.5 gamma I would use)
Ideally you want a projector that as well as having a preset for 2.5 gamma has a multi-point gamma correction system. Simple ones have three points low, middle, high. So you can adjust the relative contrast of the dark, middle, bright parts of the image, it is robbing Peter to pay Paul, but allows some adjustment to suit personal preference. Complex ones have 10 or even 20 point systems correlating to 10% or 5% steps in the grey scale, this level of gamma correction is also present on some video processors and a few highend dvd players.
Gamma figures are an oversimplification of the gamma curve. By my reckoning to support gamma 2.5 all the way down to 1% white, you would need 100,000:1 contrast, alot more to go all the way down to digital 17 and to go all the way down to 0% white infinite contrast. Projectors do not possess anywhere near this amount of contrast. To just track 2.5 gamma down to 5% white (the point at which commercial digital cinema projectors start adjusting their gamma to compensate for less than infinite contrast) you only need 1789:1 and then a little bit more for the 0-5%white, most projectors are 2500+:1, or at least claim to be, so they should be able to do this. Shadow detail will be crushed (have less contrast to black than it should) but be present. Commercial cinemas typically have lower contrast than home cinema setups in dedicated rooms because they have ambient health and safety lighting so less on/off sequencial contrast, and may have lighter decor so less simultaneous contrast. But commercial cinemas never the less use higher gamma than many consumer projectors.
Black level is also critical to good perception of image depth. You want the bottom 10% of the greyscale to be dark enough to give you a good black floor to the image. While still having a white level high enough to make images of bright sunny days or deserts look convincing. The only way to do both these things is to have high contrast ratio. You can lower the brightness of a projector by using a camera neutral density filter or grey screen to give it a better black level, but you need the contrast ratio to keep the white level high enough.
How much you see the benefit of high gamma and can use a low black level comes down to contrast which comes in three types.
Native/Simultaneous contrast, the maximum contrast the projector is capable of simultaneously showing in the best case image. How much depth bright images can have
ANSI (checkerboard) contrast, the contrast the projector is capable of simultaneously showing in a very bad case image. It also indicates how much black pixels get washed out - turned grey by nearby white pixels. So can be indicative of contrast in fine details. How sharp bright images can look and worse case depth.
Dynamic/Sequencial Contrast. Limited by the other two above, indicitive of how much the native contrast ratio can be maintained in less than ideal images. How much depth can be maintained but limited by the two above.
Note contrast is also reduced by the room. Ambient lighting washes out the screen blacks requiring a higher black level to not lose contrast. No ambient lighting enables maximum on/off sequencial contrast to be seen. Light colored walls, floor, ceiling mean light reflects off the screen into the room and then off the room back on to the screen reducing simultaneous contrast by washing out the dark parts of the image with light from the bright parts of the image. So a projector is best suited to a dedicated light controlled room ideally a black coloured batcave.
Projectors come in several types LCD, DLP, LCOS
LCD projectors with dynamic iris has good dynamic sequencial contrast but relatively poor ansi contrast ratio and native contrast ratio. The images have less depth and sharpness in ideal images but maintain what they have over varying image brightnesses. Lcd also has better placement flexibilty with lens shift, can be brighter since it can not induce dlp rainbow effect, has more compeditive pricing than dlp due to multiple chip manufactures. Lcd projectors split the light from their lamps through three colour filters on to three lcd chips then combine the three colour images together to make the image. They are easier on the eyes than DLP, but because of panel alignment may be less sharp. Lcd panels have lower pixel fill factor than dlp, more screen door effect - visibility of the grid of lines between each pixel, so you need to sit further back. Lcd projectors usually do not have sealed optical paths so may require filter cleaning, and can get dust on the panels causing blobs on the image, that may require dismantling the projector to remove.
Note human perception of contrast is partly dependent on the brightness, as the image gets brighter contsrast sensitivity increases and becomes more focused on small details. So with two displays with the same contrast but with one brighter than the other the brighter one will look like it is higher contrast and fine details will be drawn more to your attention. So Lcd low simultaneous contrast in comparison to DLP can be slightly offset due to it being possible to have Lcd brighter, due to no rainbow effect and higher dynamic/sequential contrast keeping black level dark for dark scenes.
Single chip DLP projector without dynamic iris has good ansi and native/simlutaneous contrast but dynamic/sequencial contrast is the same as native. Images can look stunning in ideal bright images but worse in darker images. Dlp usually has relatively large lens offset angle and no lens shift so placement flexibility is poor. Dlp if run bright can induce eyestrain and the Dlp rainbow effect. Dlp projectors have higher pixel fill factor - less screen door effect so you can sit closer to the image than with Lcd. The light path is also more commonly sealed and filter free, so dust blobs are usually less of a problem but can still occur. Dlp mirrors flick on/off rapidly to produce shades of grey as the eye/brain averages the light. The dlp mirrors are not capable of producing the full 8-bit greyscale on a per pixel bases, so rely on temporal (over more than one frame) and spatial (over more than one pixel) dithering in dark parts of the image, and if it has a white segment in the colour wheel in some mid-brightness shades, this can cause visible noise, you can make out the flicking on/off pixels. The faster the colour wheel the less likely dlp rainbow effect but the more likely dithering noise will be noticeable if the image is too bright. Rainbow effect can make a too bright dlp unwatchable, while dithering noise can be annoying.
Note when projectors give brightness and contrast rattings that it may not be video optomized. Projector lamps have excess green and deficit red. When calibrated for video D65 the brightness and contrast of the green has to be limited to that of the red. Video optomized DLP projectors have enlarged red segments on their colour wheels to compensate for the lamp, they give their maximum brightness and contrast with video. Non video optomized projectors claim much higher brightness and contrast than they can achieve with video while maintaining good/accurate colour reproduction. If a DLP projector has a white segment in the colour wheel it enables it too boost brightness and contrast at the expense of color saturation this is fine for presentations, but for video you are not going to use the white segment if you want best picture quality, so again the brightness and contrast figures maybe misleading.
DLP with dynamic iris, done well this should beat Lcd hands down. But DLP has been doing dynamic iris less long and some projectors attempt to implement a too aggressive version, so check reviews, in case it induces visible brightness pumping or is noisy in use. Same limited placement flexibility and limits to how bright you can comfortably go.
LCOS / DILA the best native/simultaneous contrast by a long way. ansi contrast poor. Some have dynamic contrast some do not need it. Images can have the best depth by far but are not as sharp as DLP. Same advantages in placement and brightness as Lcd. LCOS has higher pixel fill factor than dlp but like Lcd relys on three panel alignment. So the image can be brighter and viewing distance can be closer, the image looks smoother but maybe less sharp than Dlp. Some LCOS projectors have expanded colour gamuts which have the effect of making colours over saturated / over bright the further the colour is away from white, this can make the image look slightly odd, so some people use video processors with colour management systems to tame the expanded colour gamut.