AC-powered CDI is simplest. The exciter coil (charges the capacitor in the CDI module) generates a constant AC Voltage as the flywheel rotates. This is due to the flywheel having magnets all the way around its circumference. The constant power permits the CDI module to release a spark at any point in time.
A major limit when converting a magneto ignition engine to AC-powered CDI, is the flywheel having one magnet. At peak Voltage generation, the typical one-lunger fires the spark plug. Ignition timing is fixed within a narrow window of time due to this.
Contrast that designed-in timing limit to CDI, with the ability to fire the spark plug any time.
DC-powered CDI has the obstacle of requiring 12 Volts DC to power it, but the simplest engines lack the necessary charge coils, flywheel magnets, rectifier and battery circuits.
Don't let any of that discourage your experimenting! Keep us posted on your progress.
Jon