Early 5R55S/W were problematic ( broken bands, broken servo pistons, bad solenoids and converters). The 5R55N came in the Lincoln LS and were much better. I haven't worked on many, mind you I don't work at a Lincoln dealer.
The 5R55E has been around for a long time so now they are very reliable. The only real problems I've come across in the 6R60 ( 4.6 Explorer ) are programing problems. They've had a few TSB's for TCM reprograms. Nothing serious.
AX4S, 4R100/E4OD, CD4E were THE bread and butter of my paycheck back in the day. Now it's Torqshift ( 5R110, SuperDuty ) and 4R75E ( F-150) .