What a difficult question to answer.
Most commercial ballasts seem to take a compromise between Electrical Watts in to the ballast and watts into the tube. The end result is that in general there is not a lot of difference in the power in, as measured by a wattmeter.
For those manufacturers who rate for tube watts then you will see probably 10 to 15% reduction in power requirements from the electronic ballast.
As Amanda said, the hf operation gives more light and if you have a photometer you will find that for a given power in, the electronic ballast will do significantly better. Unfortunately the eye is a poor photometer and the improvement may not be so obvious.
Now to the real sting in the tail. This all applies on sine waves and you are considering modified square wave operation so what effect does this have?
Magnetic ballasts don't like these crappy waveforms, the iron losses rise in the choke, they hum and vibrate, the wattage for a given voltage changes, the power factor correction if fitted fails to correct the thing for other than a sine wave and presents a nasty load to the inverter which at best will reduce the number of lights it can run. It may kill a small cheap poorly protected msw inverter.
What about electronic ballasts? The simple things used for compact cfl rectify to dc with a bridge and run perfectly happily on msw. much more satisfactory than any magnetic version.
Not so simple with more expensive and sophisticated ballasts for bigger tubes, these ( at least in Europe) seem to use power factor controlled rectifiers that object violently to the dreadful waveform and may refuse to operate, they may blow up but I haven't had one do so. Tridonic engineers told me not to try on msw. These units all work on dc and if you rectify the output with a bridge and smooth it a bit they work perfectly BUT the dc voltage range is significantly lower than the ac range and you are likely to find the peak rectified dc is above the permitted dc rating and they may shut down on over voltage. Having to include a transformer to overcome this is a pain and so is the need to rectify at each light ( modern light switches won't handle dc so that rules out dc distribution).
Maybe N American ballasts still use earlier technology and they may work like the little cfls.
My take on this is that small msw inverters will only handle cfl or non power factor corrected electronic ballast. Big ones will run magnetic ballasts but not completely effectively. Using pfc electronic ballast requires conversion to dc but watch the voltage rating. I wouldn't trust and ballast manufacturer who is not prepared to be honest about the suitability for non sinusoidal operation.
I tend to do as Amanda suggests and run each light with its own inverter from the low voltage, but there are very few low voltage ballasts that genuinely work properly except for the little cfl sized things. I have had to build my own to get the results I want. It is all to easy to make inverters that give light but at lumens per watt that don't much exceed halogen and that seems pointless.
Sorry it has probably put you off rather than answering a simple question but that has been my experience.
Flux
