Here is a comparison shot. These have been contested at times but it does demonstrate how one screen can look and perform different from another.
In this example we can clearly see that blacks are deeper and darker than the main screen, but whites aren't taking the classic hit that happens with a lot of gray screens. In this example I would say that the screenie does show the difference between a good quality matte finish and a slightly more advanced application.
Here is one that is definitely eye candy, but I would say is a bit of an unusual thing to have taken a screenie of. The reason it was picked was the plaque. The image depth of the reflection is what I was trying to show. Keep in mind, this was taken using a Sharp presentation projector with a CR of just 250:1 on a simple OTS matte finish screen.
And then there is the argument of whites on a gray screen. Everything is relative. With a direct comparison to a white screen, yes whites will look less than white on the gray screen, but once that white reference is removed, our eyes and brain no longer have a reference point to compare things to so since we know something is supposed to be white... or even a specific color for that matter, our brain will tell us it is that color. Of if the screen itself is way off and pushing the image in a certain direction then we will start to see the color push.
Nobody can argue that this doesn't look white, but if a white screen reference was introduced then all those uniforms would really look white on the white reference and a duller dingy grayish on the gray screen. It's all relitive to our references that our eyes see.
Calibration shots and color bars though are really what demonstrates a screen, but they are boring to look at, and as Harp pointed out, they still can be very subjective and prone to a lot of variables.
Some of the variables can be the camera. Mech mentioned that a lot of camera's allow you to shoot in RAW mode, many don't though, mine included. Even if the camera does have that feature, the operator themself becomes a variable. Some people know how to use cameras, other's don't and just point and shoot... even if their camera has a ton of professional features.
I also see most screenies that are just the screen. I always like to take a bit of a wider shot that included part of the room itself so there is a reference in the shot. Not all people do this which does cause an inconsistancy between what people are looking at. Without references it is very hard to tell what we are looking at when it comes to lighting and the room conditions.
Comparing two screens that are vastly different basically can only show deficencies and sometimes that technique has been used to make one screen look better than another when in reality it's an invalid test. Neither screen is being shown in its optimal conditions, and when it comes to calibration one screen is going to suffer, or at best neither screen will be shown in its best 'light'. (Pun intended
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So I am firmly in camp with both sides of the debate. Overall screenies do tend to be eye candy, but we also can get some information out of certain ones. I'll go back to the broken record again and that being that screenies alone are fun, but when combined with data such as color balance, spectral reflectance curves, and some of the other hard data available, then we can get a very good idea of how the screen performs overall.