MFrey

I have both the mark 1 and mark 2 versions. The mark 2 version is sharper across all focal lengths and out to the corners (especially @ 55mm!) and much lighter. Although it’s lighter the build quality is just as good. I’ve compared the zoom on both marks, and the mark 2 is quite smooth and even. I’m extremely happy with the new version and will be selling the mark 1.

Yeah the 17-40 wasn’t announced when I purchased mine so didn’t have that decision.  I went with the mk II as I was impressed with what offered and the amount of size reduction they managed. 
 
I saw this that has pretty good comparison between the mk II and the 17-40
https://fujiframe.com/articles/sigma-17-40-vs-16-55-fuji
 

I have the mark 2. The zoom seems perfectly smooth to me, but I don't shoot much video. What I can say is that it is a lovely lens. Much better in every way than the 16-80, albeit a smaller zoom range, in every way.

I really like the image quality, size, and weight of my mark II. I never owned the mark I so I can’t help with comparison though it is highly regarded as a great lens.  I don’t use mine for video but I will say it doesn’t have the smoothest zoom, which seems to be common complaint for the mark II.  For photos it doesn’t bother me but I would imagine would be an issue if zooming while recording video.