Paul,
It is pretty easy to compare Flats using the same software you use for image processing. You simply treat one of the Flats as if it were an image. (Just think of it as an image of a flat blank illuminated wall which it is.) You then perform a Flat Field Calibration using the other Flat. I did the following in PixInsight.
Important! I am assuming that each of the Flats you showed in your post were Master Flats which had been calibrated and then stacked. If they are raw single uncalibrated Flats right out of the camera, then things could be very different although the analysis procedure would remain exactly the same.
Below are brightness contour plots of the Flats in question. These contour plots make the brightness profile differences in a Flat very easy to see and visualize. They greatly exaggerate the brightness differences in the image.
The first row depicts the brightness profiles of you Sky Flat (on the left) and your Wall Flat (on the right). As can be readily seen, the Sky flat looks just like you would expect a flat to be. It shows the dust motes very clearly and also allows you to see the contours of brightness caused by vignetting in the optical system. Other than being slightly off-centered, it looks perfectly acceptable. The off-center nature is probably real and may represent either a very slight off-axis collimation error or tilt at the focuser (which is pretty common). It is sight enough not to be a concern.
The issues that @lambermo described above are very easily seen in the Wall Flat brightness contour plot on the right. There is a brightness gradient from roughly bottom to top. In addition, there is a very abrupt slightly diagonal gradient in the lower portion of the Flat. That may be shutter sweep if your camera has a built-in shutter taking a short exposure or it could be from uneven illumination within the light panel itself.
The second row of the attached image shows the brightness contour plot of the "flattened" Wall Flat. In other words, this is what you get when you flat field calibrate the Wall Flat using the better Sky Flat. In PixInsight, this calibration was done in PixelMath using the standard flat-fielding equation:
Flattened_Wall_Flat = Wall_Flat / (Sky_Flat / mean(Sky_Flat))
You can do this operation in any software by simply loading the Wall Flat as if it were a Light frame and then running an Image Calibration using the Sky Flat as your Flat. You do not need to supply a Dark frame at all since the both Flats will have been previously Dark or Bias calibrated already. Ideally, the bottom row image should be close to be very flat and evenly illuminated. It is not and that is a problem. The brightness contour scale at the right shows the "Flattened" Wall Flat to have about 19% illumination difference across it compared to the Sky Flat.
I would say that you need to investigate a little more to find the reasons for the issues with the Wall Flat before using it to calibrate image data.
John
Edited by jdupton, 28 November 2022 - 05:35 PM.