I have not read this whole thread, so I apologize if I am repeating info already posted, but I have measured the ST 130 and the original Firehawk, which I own. I can offer more than an impression.
My PJ is mounted 2 times the screens actual width away from the screen. The PJ is mounted .16 times the screens actual height above the top of the screen. The Firehawk is 9' wide by 5' tall. The PJ lens is 18' from the screen, and is about 9.5 inches above the top of the screen. The PJ location influences the measurements, and mounting the PJ in a different location relative to the screen will result in different measurements. I have read that the Firehawk was designed to be used with a ceiling mounted PJ. In my setup, it imparts almost no color shift (less than .002 in x or y) compared with measuring the light directly from the lens of the PJ, and was actually slightly better than the ST130 in this regard.
If the ST 130 sample that I measured is 1.3 gain (as rated), then the Firehawk screen that I own is 1.0 gain measured at the center of the screen. The Firehawk that I own imparts almost no color shift at the center of the screen. HOwever, as with all high gain screens it does hot-spot (as does the High Power mentioned in one of the posts directly above). It also imparts a color shift to the image as one measures away from the center of the screen. This seems to happen with every high gain screen and the higher the gain, the more severe it is. The ST130 also hot spots and imparts a small color shift as one measures near the perimeter of the screen, but to a much smaller degree.
The rest of this post is my opinion of what all this means when it comes to selecting a screen material and determining screen size:
1. The most important thing in selecting a screen is to end up with the proper screen brightness with a new bulb in the PJ. Somewhere in the 12-18 fL range allows for bulb aging. In a light controlled theater, most folks in my experience find that a PJ is bright enough down to about 7 fL. Unless you want to replace your bulbs prematurely, account for bulbs dimming with use. Achieving proper screen brightness is more important than the other considerations listed below combined. It is a mistake to use a screen that is too large or too low gain. Don't compromise on this.
2. The Firehawk is visibly better at quenching cross-light reflections than an ST130. It does not take a trained eye to see this. It is readily visible in actual video. If your HT has white walls, the Firehawk will yield an image with greater ansi type of contrast. The greater the amount of cross-light reflections, the bigger the Firehawk's advantage in this regard. If your HT has dark and/or non-reflective surfaces, this advantage becomes insignificant. It might still be measurable, but it isn't visible, IMO.
3. No screen can increase a PJ/image's on/off CR. This is a misconception that one sometimes reads on the forum and in screen manufacturer's literature. The only affect that a screen can have on contrast is what has been covered in point #2 above. Compared to an ST130, a Firehawk will yield darker Blacks and darker Whites, and both to the same degree.
4. A grey screen does not make an image grayer. It does not make colors dingy. It only makes the image less bright compared to a higher gain screen. In the video world, grey is the same color as white, it is just less bright. An ISF calibrator sets a PJ's "greyscale" so that from Black through all levels of grey all the way to White the PJ puts out D65 White (or as close to it as the display is able). I use a spectroradiometer to measure light reflected directly from the screen as part of every FP calibration. Calibration sets a PJ so that the colors coming off the screen are identical, regardless of the screen type (grey vs white).
5. How much should one be concerned with hot-spotting when selecting a screen material? The reason I listed this consideration last is because it is the least important consideration. Don't compromise on the considerations above to address it. Not one individual has ever seen the hotspotting from my Firehawk, except me. I only see it occasionally in actual video and I only started seeing it after I learned that it is there. I have not had a customer with a Firehawk ever complain about hotspotting. The only exception has been if they watch the calibration, because it is readily visible in a full field grey test pattern. THe same is true for the color shift imparted across the width and height of the screen. It is not visible in actual video. These defects are caused by the high gain coatings used on high gain screens. So the benefits of high gain has some trade offs, but they are worthwhile if you need the gain.
To summarize. If you need a high gain screen to achieve proper screen brightness at your desired screen size, then either use a high gain screen material or choose a smaller screen size. If you have white walls in your HT (or ambient light issues) the Firehawk will yield visibly better image contrast, but should only be used at a size that gives proper screen brightness. Otherwise, use a higher gain material and forego the Firehawks advantage. If your HT has light control and dark and/or non-reflective surfaces, use the screen material that results in proper screen brightness. The Firehawk has little advantage here, and there is thus no reason to suffer its hot-spotting and color uniformity (at different viewing angles)performance, even though those issues are difficult to detect in actual video.
The recommendations above are prioritized by how visible the different types of problems are to the typical viewer. The biggest mistake I see in HTs is using too large a screen for the lumen's output of the PJ. Often this is done at the insistence of the customer against the recommendation of the custom installer. This is correctable by using a higher gain material or a smaller screen. Both of which are preferable to the image being too dim.