agx also comes with a preset that uses the same primaries tweaks as sigmoid | smooth. Of course, the curve is still different, and per-channel curves influence not only contrast, but hue and saturation.
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I know, I consciously chose the default settings in agx, so it is belnder-like. But maybe it would be more appropriate to choose smooth in this case, because sigmoid has the smooth preset.
I knew the darkest sky was Filmic, as thatās the only way I know to get a lot of highlight color in the sky (like the clouds of the sunset) and still get details.
I had no idea about the rest tho, since Iām waiting to first try AgX in 5.4.0
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If you are playing a guessing game, yes. If you are using the module, no. 
Itās not that the blender-like (or scene-referred default) preset is superior, itās only that the āout of boxā config of agx uses Blender-like primaries.
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I think I just realized: filmic was finished in 2019, or december 2018 - it was quite advanced considering the fact that that was already 6 or 7 years ago. I mean itās still usable. Sigmoid and AgX are better, but not so much better. Oh man time fliesā¦ so many things changed since thenā¦
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Actually I think v7 was introduced or committed around April 2023ā¦ not that it matters
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I would have say also Filmic, Sigmoid, Agx (easy now ā¦ )
Why :
For my personal taste, Filmic is the best for blue sky, and here, the first one has the most saturated blue sky
Sigmoid and Agx are probably better for midtones and shadows ( better gradation in shadows) ā¦ and Agx is a kind of āsuper Sigmoidā ( more controls).
Filmic is also less saturated and I often add some with colorbalance.
And with my Olympus, I prefer greens from Agx than Filmic.
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When you change sigmoid to ratios instead of per channel it will give the sky a bit more but then thatās the method filmic uses and the color changes in a similar fashionā¦you also lose the primary controlsā¦ Iām not sure if anyone uses it or its just in there for comparisonā¦
I havenāt read the other replies yetā¦
_02 definitely filmic - based on the saturation-preserved blue sky
Other two not so sure.
Theyāre both doing the nice AgX-style highlight rolloff that I like.
Iāll say _03 is sigmoid based on the shadow contrast and _02 (the last one in the post) must then be sigmoid.
Howād I do?
Edit: I see @siamak got it right congrats!
How are we identifiying the images? The order from top of post, or the file name suffixes?
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Thank you
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For me, filmicās default skies are often oversaturated and dark, so I drag the saturation control to the left.
In agx, you get a global saturation control in the look section, as well as per-channel controls on the primaries page. Since itās essentially a per-channel curve, contrast also affects saturation.
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All this stuff sounds so esoteric when youāve only used RawTherapee, in which tone mapping is (at least for me) mostly done withā¦ wellā¦ a āTone Mappingā tool. 
The docs says āThe method used is taken from Edge-Preserving Decompositions for Multi-Scale Tone and Detail Manipulation with some modifications.ā Dunno if itās even close to one of the three mappers presented here.
(Like many others it seems, my fav is the middle one. Looks like a very tricky picture to process. 
)
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For me, the filmic version lacks a whole bunch of three-dimensionality, especially in the parts where the leaves meet the blue sky. The filmic version just looks way āflatterā there and even somewhat āwrongā, especially if you flip between the versions. Hard to explain it with words, but the two other versions seem to better convey the depth.
Btw, stunning picture @betazoid !
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As I understand it, ātone mappingā has different meanings. I think the tonemapper in RT (of the kind under discussion), if I remember correctly, is the main automatched (or manual) tone curve.
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I and most of users are new to Agx and I personally like it specially after your tips on the negative films. Results are amazing but one needs to tweak the defaults to achieve the good results. I am sure dt experts soon will publish there workflow with it. I myself slowly understanding effect of the sliders. Now I am moving to primaries tab. Once I discover the good starting point for my taste for any photos, I will save it as preset/default.
Looking forward to the completed documentation on Agx.
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The settings can go in all directions but as I understand it much of the secret sauce is in those pre tone mapping color adjustments in primaries so if you zero them or modify them substantially then you might be losing that ā¦of course over time and with practice the use of each slider and crafting the look you want becomes more apparent and you have to experimentā¦
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Thanks!
So the computation-intensive āTone Mappingā module would be something else entirely? 
Tone Mapping - RawPedia
Appart from the stuff about bringing out details, it seems to match Tone mapping - Wikipedia relatively closely. 
I would have said
Filmic,
AgX,
Sigmoid
Filmic is obvious by how saturated that blue sky stands out. AgX and Sigmoid are less clear (and I got them wrong), by how much that sky is desaturated.
Now knowing the correct order, I like how natural AgX rolls off the highlights, and how it keeps saturation in the midtones.
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Iām still not sure what module adjustments were added to the three reference edits just that there was an attempt to make them similarā¦I think agx will generally offer the most details in the shadows as a give away and filmic the sky will have more color, For rough comparisions of the modules likely it needs to be just the defaults with default or the same exposure for a comparison of the starting lookā¦or maybe only adjustments you can make in the module to take it beyond thereā¦
I took the recent playraw for the path in the field of grass and golden rodā¦
I applied the 3 ā¦I bumped exposure a little and then for agx only the pickers for white and black and the pivot.
Again the picker for filmic and for sigmoid I was going to tweak just the skew to match the DNR but it was similar out of the gate so I left it.
Those images showed some of the differences you might get by default with color and tone esp for shots with lots of green (for the example I used)ā¦of course any further tweaks or module differences start to break down a strict comparison of the tone mappingā¦
In general, the filmic colors were colder, sigmoid had much more midtone saturation esp in the greens and reds and agx was sort of in between for saturation but more in the same color palatte as sigmoidā¦ I didnāt post them as I didnāt want to divert or hijack anythingā¦
All the tonemappers can get help from other modules so maybe the best comparison is other than denoise and lens correctionsā¦all you can use is base exposure and the tonemapper and then pick an image or images and see where you can take itā¦maybe comparing the defaults and end results for eachā¦
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