I have a brand-new roll of Agfa Vista + in front of me and it states that the film speed is ISO 200 . 24ᴼ so the logarithmic DIN system is still in place on modern films.
As I use a number of quite old cameras, I always use the DIN figure as the ASA system changed drastically in the late 1950s and meters from before then have DIN 21 equal to ASA 40, rather than ASA 100.
It is not quite right to say that ASA was arithmetic and DIN was logarithmic (although that is correct) as the DIN system used (uses) a very different emulsion characteristic to measure film speed than the ASA system did. A large ASA difference in film speed between two films would not necessarily mean a large DIN difference. The DIN system (or degree part of ISO) measures a fixed density above the fog level while the ASA system ( and first part of ISO) is based on the gradient of the log exposure/density curve. It is at least theoretically possible for one film to be faster than another according to DIN and slower according to ASA.