Bruceynz:
The suspension that Chrysler implemented in 1957 used the longitudinal torsion bars that ran (roughly) parallel to the frame rails. The torsion bars in those cars are pretty much straight, running front to back. It was used across all body lines until 1976.
In 1976, with the introduction of the Volare/Aspen, Chrysler had a completely redesigned front suspension, using "L" shaped torsion bars that ran across the width of the car (perpendicular to the frame rails for part of the "L"). This same suspension system is used in all F, J and M chassis cars, unless modified by later owners. THis is the transverse torsion bar front suspension.
The suspension is fine for almost all street driving, but does have less perfect geometry than the older longitudinal torsion bar system. There was a lot of opposition to the new system within Chrysler due to its less optimum geometry. The true reasons for the redesigned front suspension would probably never be known, but some reasons that have been put forward are: quieter, smoother ride; easier to assemble due to the entire front suspension being one piece with the K member, so the entire front end of the car would be installed in one step with the K member and engine; fuel savings due to the overall system being lighter and allowing for a smaller car with big car ride; and I am sure others. The front suspension did get a bad reputation, due not to the design, bu the first year or so of the Aspen/Volare, the K member steel thickness was so thin, that the K member would actually deform over time, throwing the wheel alignment off, and eventually, running out of wheel alignment adjustment so that you couldn't bring the alignment within specifications. The thicker K member fixed that, but a lot of damage to the reputation of the Volare/Aspen, that front end design, and Chrysler, had been done, even after Chrysler fixed the issues.
The first suspension (longitudinal) design is the one that is held in highest regard. The later one (transverse), while a good one after all of the fixes were put in, is nowhere near as good (too much camber change over the front wheel travel up and down, from what I understand).