Well, I am sure Sean is right at some level...
However, I am feeling just fine about my '72 Bavaria with BW65 Auto trans...
As soon as I could (after fixing a few more critical bits) I bought 6 gallons worth of a basic F-type ATF like this:
https://www.amazon.com/Amalie-160-6...=1528418110&sr=1-1&keywords=type+f+auto+trans
Made multiple drain and fills (about 5 quarts at a time), and toward the end of that process I replaced the filter/screen and gasket with a kit like this:
http://xks.com/i-6920316-jaguar-filter-kit-a-t-bw-65-66-alloy-xj-6-series-ii-iii-12-0400.html
Cost not too much, took not too long, and I have put in about 3,000 miles so far with fairly smooth and totally reliable shifts. Sure, it's still a classic slush-box...and you have to drive with both feet until the engine is fully warmed up. But it works, and is kind of convenient in stop and go traffic. And I do think the 3 speed auto transmission somewhat limits your ultimate top speed...mine won't really go much past 90 mph.
But I can accept that. And at the moment have other things demanding my attention.