I got a PM question regarding the photos I posted so here is the answer and explanation.
The photos I posted are of my oscilloscope displaying a multiburst test pattern from my Accupel HDG-4000 test pattern generator. To get the scope to display the pattern, the green BNC from the HDMI to RGBHV transcoder was connected to the scope input. A multiburst pattern looks like the image below when shown on your projector screen.
What the multburst pattern shows is the bandwidth of the device being tested. The black and white alternating lines start out wide on the left and then get narrower and narrower towards the right side of the pattern. At the right side with the thinnest lines, the black and white lines are literally one pixel width wide. Since the lines are only one pixel width wide, they represent the maximum resolution of the device being tested.
The scope photos show 1080p 60Hz. What you see on the projector screen is a black and white alternating line. The scope shows the rise and fall of these lines as they go from black to white and back and forth.
Ideally, when you look at the multiburst on the projector screen, the 1 pixel wide lines would be just as bright as the lines that are very wide. In real world analog this is never the case.
However, what you want to see is a transcoder that does as good a job as is possible. If a transcoder were perfect, all the lines in the burst pattern from the thick ones to the thinnest ones would be exactly the same height (amplitude) on the scope.
What you see on the Moome box is that all the lines are the same height except for the very finest 1 pixel wide lines. What you see on the HDF3 is a kind of hour glass shape to the different width lines and the tightly spaced lines (high frequency) are not nearly as tall as the wide lines (attenuated). This means that the image can not be as sharp because the bandwidth is attenuated before it hits the projector and you can't properly draw edges of objects (softer).
Another observation from the scope shot is that there is a lot of noise and irregularities in the HDF3 multiburst. You can also see a lot of peaking (edge enhancements) on the high frequency part of the burst on the HDF3. The Moome box does not have these problems either.
On a 7" projector this won't really matter, on a good 8" projector it will make a difference, and on a good 9" projector it will make a huge difference.