I use inverters exclusively in my home...while its quite hard to compare their power saving feature (becuase I don't have another "control" home that I can compare with), by rough estimates, if I compare with my uncle's home: I run higher capacity units for ~10% longer and my electric bill is only 60% of his.
Again these sorts of comparisons are hard to do, becuase I don't know exactly how long he's running his ACs, or even what the runtime is in my home. But the point being that yes, I do feel that they save money. The amount is up for grabs.
Just one piece of advice: if you do decide to buy an inverter unit, you have to run it for a while before it's power saving features kick in. I know a lot of people, only turn on their ACs for an hour or two...in that case it isn't worth the additional cost of an inverter unit. Also, set your unit at a reasonable temperature (eg 25C), not the minimum that some leave it at.
I have a mixture of Panasonic and Toshiba units. They all work fine.