First a general image of what the port situation at the ISS kind of looks like. This is a bit dated, but one of the best images, showing some of the possible vehicles docked.
To note the ATV at the left end, the Soyuz/Progress up/down are all using Russian segment ports.
The HTV on the right, next to the Shuttle is where a PMA now resides with an IDA. The Shuttle port has had an IDA added to it.
On to the question, right now, only the Russian Soyuz and Progress vehicles dock automatically, and they continue to use the updated Kurs. There is a manual backup mode that is seemingly being used more often than would be liked of late. Progress, no crew on board can be remotely piloted/docked from the ISS itself.
Thus the goal is pretty much always dock as automated as possible.
Dragon, Cygnus, and HTV (JAXA) all berth, where the fly to a holding point and the CanadArm2 grabs and completes the berthing. This holding point is an automated process, but a human flies the arm to grab the vehicle and then berth it.
A core difference between berthing and docking is that the actual connection of vehicle to station for docking can be done automated, such that a crew abandoning an empty station, can close the door behind them and leave. A berthed vehicle needs someone on the other side to fully close the door and thus someone needs to stay on the station. So even if you automated the berthing, you still need someone to open or close the door.
The future Dragon Crew (Dragon V2, whatever it officially ends up being called) and Boeing CST-100 will be using a US automated docking system when they dock to the PMA ports (with IDA's attached). (As I write this, Nov 2018 flight of Dragon V2 first expected. We shall see).
The Shuttle (retired) used the PMA's as well, but without the IDA adapters that were recently added (Brought up on Dragon Cargo missions).
The ESA ATV (retired) used Kurs to dock to the Russian segment ports.