Fist off all, there's three coils on the stator:
1. Pulse coil - provides the trigger signal to time the ignition
2. Lighting coil - provides power to charge the battery
3. Charging coil - provides power to the CDI to do its thing.
In a completely stock setup, the spark power is dependent on RPM's and what the charging coil puts out (which is RPM dependent.) Once the ski is running, you can disconnect the battery and the ski stays running - because the CDI gets power from that coil, not the battery.
In any aftermarket CDI, it gets its power directly from the battery. Spark power is not RPM dependent because of this. If you disconnect the battery while it's running, the ski will stop. This provides better spark consistency through the RPM range.
CDI stands for capacitive discharge ignition. It works like this: you send a certain DC voltage to a capacitor circuit that will greatly increase that voltage (while decreasing current - it's a trade-off. And because energy = voltage * current * time, only an initial higher current and voltage AND/OR more time will increase energy) A semiconductor circuit then takes that voltage and releases it to the coil when the pulse coil signals it's time to spark. The coil again amplifies the voltage at the expense of current)
The stock CDI circuit is designed to work with the minimum voltage that the charging coil puts out at low RPM.
Aftermarket ignitions that draw power directly from the battery do not have to work with that limitations. Their capacitor circuits can draw more voltage AND more current to produce more energy. In MSD (Multiple Spark Discharge), it also produces spark for longer, again increasing the energy).
So those aftermarket ignitions provide a higher energy signal to the coil in the first place, whose only job it is to increase the voltage given to them (energy stays roughly the same).
If you put in a coil with higher windings ratio, you don't get more energy, but more voltage - which can jump a bigger spark plug gap which increases the sparks exposure to gas/air mix).
Hope that clears it up.