I spoke to our local Honda dealer who is a friend of mine (he is biased I know) and he suggested that the cheap units can affect things like air conditioners and he has heard of cases where the air conditioner motors have been burnt out?
Hey Kev
There are a couple of issues with the cheaper ones.
There can be issues with a modified sine wave inverter generator as this does not produce a pure sine wave output, just a square type wave. Some devices like rectifiers and microwaves require the full voltage at the peak of the sine wave otherwise it may not be able to run correctly, hence drawing through more current and possibly burning out.
Also the cheaper ones have issues when you need to get them serviced as the parts are not easily procured and a lot of the agents won't touch them.
Yamaha and Honda are full sine wave inverter generators with service backup if something goes wrong. I have a Yamaha EF2400is that is a bit heavier but has enough power to run everything including the house when the power (often) fails where I live.
Couple of previous posts HERE and HERE to get some more information from...
Cheers.