Watched La Haine (4k version) the other day and was captivated by how the British Film Institute gave the film a much lower contrast soft look in comparison to Criterion's hard contrast look. I know lighting plays a vital role but did they add a filter or lower the whites?. It seems as if there is a glowing outline around body figures and objects, so did they use HDR? Has the clarity tool been used too? I'm not planning on using any type of mist filters because it will strengthen the highlights too much and this is something that I don't attend to aim for.
I think what is really making the difference here is a misinterpretation of a colour profile/icc. The darker version might be Rec709 being misinterpreted as sRGB - one is a video profile, the other stills. In colour these are similar, but the gamma curve is different. Misinterpreting will skew the darker end of the scale.
Dropping both of these into Photoshop, you can approximate a curve readjustment using Levels
Click for full size
A very hasty Levels tweak of the darker image on the right, with the untouched lighter image on the left.
Lift the blacks, expand the mids by dropping the mid-point lower down the scale.
It's not perfect, but it's close.
It's never going to match perfectly because we're not truly inverting the curve that was misapplied, but as an approximation I think it's OK. If we were to be a little more finicky, the left [4k] image is not strictly black & white/greyscale, it has a little warmth added.
You can do this for stills or movies, FCP & DaVinci have very similar controls.