The thyristor flash design is about saving unused capacitor charges. It is only indirectly related to flash autoexposure.
The CAT flash-autexposure system relates to object-distance, the succeeding systems relate to object-reflectance.
The CAT system is thus the more objective one.
However it is technically complicated in that it neccesitates a dedicated coupling between lens, camera and flash.
You're right on both points. I called the CAT unit 133A, but it was the 133D, and I bought one with the coupling ring for my FTb and 50mm f/1.4 not long after it came out. The system was actually a "match-needle" flash exposure system: the camera's meter needle was coupled to the distance set on the mounted lens through the added contacts at the hot shoe's rear and the coupling ring mounted on the lens, with the user adjusting the f/stop for proper flash exposure. The CAT System had drawbacks. The 133D dumped at full power every flash, and wasn't a very powerful unit, so Its recycle time was 6 or 7 seconds at best, and its guide number of 60 in feet at ASA 100 limited what I could do with it. In addition, setting up for CAT System flash shooting involved mounting the coupling ring properly on the mounted lens, making sure the selector switch was set for the proper lens [there were two rings available, one for the 50/1.4-35/2 combo, and the other for the 50/1.8-35/2 pair], then connecting the coupling ring to the shoe-mounted 133D. IIRC, the FTb's meter switch had to be "OFF" for CAT to function. Refocusing more than a bit meant re-setting the f-stop to maintain good exposure, slowing response time.
By comparison, when thyristor auto-flash units hit the market, I just mounted one on my FTb, chose the desired f-stop based on the desired distance range and ASA of the loaded film, and set the shutter speed; as soon as the ready light came on I had only to focus and shoot. Many units had audible signals indicating they were ready to fire as well as for exposure confirmation, allowing me to stay at the viewfinder and concentrate on shooting. The flash tube technology advanced as well, and shoe-mount units with ASA 100 guide numbers in the 100-120 range became commonly available and affordable.
Canon apparently recognized the CAT System's limitations, and never offered a higher-powered Speedlight. When the AE-1 came out in 1976, dedicated auto-flash with thyristor units was the standard. My 133D spent a lot of time gathering dust on a shelf, replaced first by a Vivitar 281, a non-thyristor high-power shoe-mount self-contained ni-cad unit. The 281 didn't last long, so I soon got a more modern thyristor unit powered by AA alkalines that I could use with both the FTb and as a dedicated unit with the AE-1 I bought in 1982.