I have played around with these over the years and have a few. The Sachs is nicer than the Bendix In my opinion and will eventually go a Moulton takeapart project. No cables is the plus for that application.
What has happened with the new Sturmey fixed 3-speed?
Kick back hubs were made by Bendix and Sachs. The Bendix models were used by Schwinn and other American makers. There were actually three different models of kick back hubs made by Bendix, identified by different color bands painted onto the hub shell. One upshifted when kicking back, one downshifted when kicking back, and the third used a different brake mechanism (friction discs vs. brake shoes).
I bought a Bendix Automatic red band hub at a swap meet several years ago. I disassembled it to find that the indexing spring had broken. This is the most common failure on these hubs. I was able to find a replacement spring from a balloon tire bike collector who lived three blocks from me (imagine that!). It still sits in a parts box, waiting for the right project for it to be used.
I was truly amazed at the quality of the workmanship of this hub. All of the parts were very well made to last a lifetime (except for the spring). Being completely made of steel, it weighs a ton (figuratively).
There were rumors that the Czech company Velosteel was going to resume manufacture of the Sachs two speed hub, but their website doesn't mention it. They are producing the old Sachs Torpedo single speed coaster brake hub, offering options on hub drilling and spacing width.
Prior to the Bendix Automatic, There was a two speed coaster brake hub made by Bendix which was shifted by a lever. I have one of those that I bought at a swap meet, but I haven't had it apart yet to investigate.
Automotive companies were involved in bicycle parts manufacture in the US up through the 1960s. Along with Bendix, New Departure made coaster brake hubs (single and multi speed), Dana made multi-speed add-ons which replaced the one piece crank internals with a three speed planetary gear system, and Stewart-Warner made speedometers for many bikes.