In case you have missed the discussion (with examples) in the development branch, here is a link to it:
https://discuss.pixls.us/t/raw-challenge-backlit/1676/50?u=claes
Well… There is only one way to find you, right? 
Either you do it - or I do it – or someone else makes the comparison…
From what I have understood so far, DT/LUT module and G’mic/custom 3D LUT are not intended to do the same thing (even if they probably in certain cases are able to perform identical tasks).
I thought the DT LUT was 2D? I could’ve read it wrong.
That is actually one of the questions I have as well… for what I can understand, with modules basically map the RGB value of some given reference patches to another RGB value, and interpolate the values in between. So for me the basic functionality is the same, but I might be missing something.
I think that the DT LUT is also 3D, because it maps RGB values into RGB values (so 3 values into 3 other values, hence the definition of “3D”). It is true that the patches are arranged into a 2D plane, but that is to my mind only a UI visualisation.
There exist also 1D LUTs, which apply the same transform to the three RGB components (more or less like tone curves do…).
I’m not an expert, so I might well be wrong. Maybe some DT or G’MIC expert can clarify this? I evoke @houz and @David_Tschumperle to help us here…
I’d love to play with this tools, but I have zero time at the moment 
Yes, the darktable LUT is 3D. That’s all I can say, comparing it to GMIC is not possible for me as I never used GMIC and have no clue about its LUT capabilities.
There is an important difference between how DT and G’mic handle a LUT change.
Example.
Here is my original test strip:
I wanted to change yellow into black, and blue into white.
Here is the strip after treatment in DT, using the new module Color checker LUT:
And here is the strip after a G’mic session, using Customize CLUT:
Hopefully, these results are self-explanatory…(?)
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I think they are kind of self explanatory: Either they use (very) different interpolation (may be true) and/or the number of points used is different and somehow automatically predetermined in Darktable (may be true as well).
What they do not explain is what we can use them for in photo processing. To get useful answers from the devs that know only one side means we have to ask more specific questions: what is the intention behind the module, what are typical use cases, how is it implemented (interpolation method, transformation, ui) etc.
A wiki post has been started to give an overview of G’mic’s 3D LUT feature over here [Article Idea] Customize CLUT - #2 by paperdigits
You can contribute!
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@Claes, how many keypoints did you use in G’MIC for your test? With 0 keypoints (Lock uniform sampling) you always get a black and white result. You have to start with at least 8 keypoints. With different settings in the total of keypoints, you get a different result.
With 8 keypoints:
with 64 keypoints:
With 0 keypoints (None):
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My impression, to be confirmed by developers, is that the G’MIC tool allows to ignore certain patches, while if I understand correctly in the DT case all the patches are always considered, also those that are not changed…
I see u use spatial regularization, I didn’t. that’s also a difference. I picked my yellow with the color picker, I think u used Red 255, green 255, blue 0 for pure yellow. My yellow was not pure, I think.
Moin, houz!
That is an interesting variety – but as soon as you delete a patch, the colors of the image will change.