1% distortion quoted above by Eric is a very nice number. Both types
of inverters square and sine can cause problems with noise. Do not
confuse high frequency switching noise with lower frequency harmonic
distortion that you would get with square waves. They are not the
same. Noise can come from many different sources within the inverter.

Inverter usually has a small switcher running to generate logic
supplies, fan voltages, and other various houskeeping chores.
Inverter may also have microprocessor dsp, or a simple microcontroller
that runs on MHz clock
Inverter may actually have an intermediate inverter switching at 100kHz
or more to get the low level dc up to a higher dc level compatable with
your AC mains voltage.
Finally the actual output sine or square wave is generated by switching
a big mosfet or IGBT that has very steep edges. 5,000 - 10,000v/us is
a reasonable dv/dt to expect. All of these noise sources will
contribute to the overall problem.

Various techniques are used with inverters in order to mitigate both
radiated and conducted EMI. Proper grounding, routing of wires,
sheilding, and finally filtering are all tools of the trade. Best bet
is to try and minimis=ze it at the source.

For the casual user best bet may be to start with a manufacturer that
others have recommended. Exeltech? LC filters to clean up the output
will help. Can set the filter to just above 60Hz and should do nice
job. WWW.CWSBYTEMARK.COM might be a good source for toroidal powder
iron filter cores.Series traps (directly across the output) might be a
good approach if the noise spectrum is known. Mounting the inverter in
another box could help. Mounting the inverter in a remote area and
using a longer extension cord could help. Wrapping the extension cord
around a Hi Mu core where it enters the shack might help as well.

I design large high performance inverters for a living, but I try to
buy gear that will run off of 12v.

Regards,
Bob