Now I have really compared a lot!
I compared Base curve, sigmoid and AgX.
They all have their advantages and disadvantages. At least from my point of view.
Base curve:
pro
It’s really easy to understand, you have the choice to steer the curve exactly the way you want, exactly on the position you want
contra
On pictures with a HUGE dynamic range it gets hard to steer it EXACTLY the way you want (@kofa already described the problem)
Sigmoid:
pro
I’m used to it. Nice handling of contrast in the midtones.
contra
often a lack of saturation (easy to correct). Highlights often look somewhat dimmed and unnatural (a bit harder to correct but possible)
AgX
pro
not much modules needed and just a few sliders in the module. Therefore easy and quick.
conta
The sliders affect each other. So it’s always some fiddeling needed. Sometimes there is a small hue shift (especially in the blue tones).
Conclusion (so far):
All three methods work well and it is possible to achieve similar if not nearly identical results.
Anyway for me there are two winners:
AgX and surprisingly, good old base curve. Both have the advantage that I am able to get really fast to where I want, without to many modules. Which is very important for me.
So AT THE MOMENT I tend to use base curve for pictures with a normal up to a higher dynamic range (simply because I’m able to steer the curve exactly the way I want and the colours are treated more the way I like).
For images with a high and extreme dynamic range I will switch to AgX.