There are many good reasons that having a physical filter is better than emulating the effect in post. I'm considering filters myself, although I have lenses that have some of this effect built-in so I'm not starting with a blank canvas.
As pointed out in the thread though, lighting conditions and subject matter can make the effect very difficult to control. For example, if you had a strong light in the frame then you might get a huge amount of the effect, compared to a shot with low contrast and no light hitting the filter which might have almost no visible effect.
Therefore, to get the two shots to match visually you would have to swap the strength of the filter on each shot to get an end result that looks the same. This is one of the advantages of doing it in post, because you can adjust it afterwards, and don't need to buy every strength of filter, and you can even select values in between the ones that the filters come in, or even animate the effect so that it varies amount in the same shot. For example if you went from a portrait shot and panned to show a scene with the sun in it then you would want more effect at the start of the shot than at the end, and a smooth animation would do the trick in post.
I suggest that the best approach is likely to combine the two, getting the majority of the effect using a filter while shooting, but evening it out in post.
The word "Black" in the filter's name refers to the tiny black particles embedded in the filter to absorb light that scatters sideways through the diffusion, thus reducing "glow haze" and "halos."
This black particle technique first appeared in Harrison & Harrison Black Dot diffusion filters.
Black Promist is one of the best "mist" filters that preserves contrast, especially in the blacks, hence its name. I think it is money well spent to have a 1/8 or a 1/4 black promist in your bag. I haven't used any of the other filters.
