Number one is that they self destruct if the ignition is left on without the engine running. This will fry the module and melt the coil. I do not know if the Pertronix III has resolved this issue.
As far as I can remember, that was already solved on the Pertronix II.
When the Pertronix unit does work, it is as good as a fresh set of properly adjusted points. Not better, but just as good.
There are some things, that points can't provide though;
Adaptive dwell throughout the entire RPM range
More available energy between 3000 and 5000 RPM, and 2 times more available plug voltage.
Compensates for inherent electronic delay by adjusting the spark timing throughout the entire RPM range.
Synchronized peak current and spark timing
Startup sensing and more energy for quicker, easier starting
