Most traditional or conventional generators do not produce "pure sine wave" AC current especially the ones made in China or the cheaper ones, I can prove that to you sir. Try feeding the output AC current to a motor and you'll see what I mean. I've had a job in a manufacturing plant before (Sanyo) where we run motors (stepper, NEMA) and the genset we used were sourced from Japan (mostly Honda's) and produces "pure sine wave" AC current so sensitive loads (motors) can run efficiently. Newer quality gensets especially the inverter types are the ones which can produce "pure sine wave" AC current. Right now I work for an electric utility company which supplies electricity to industrial customers such as feed mills and water pump stations which obviously have motors.
They might produce output that deviates from a clean sine wave, but I don't see them producing a "modified sine wave" like how a modified sine wave inverter would (with defined steps). The deviation is mostly from the lack of consistent spin rate for the alternator (due to lack of rotating mass, bad tolerances, poor transient compensation, etc.), and sometimes because of the characteristic of the load.
Good inverters can provide a very clean output that is very close to a perfect sine wave. Low cost inverters can provide a very dirty output (square wave or stepped square wave... aka modified sine wave).
Conventional generators use an alternator that should always output something approximating a sine wave. They do not have the capability to produce a square waveform.
Modified sinewave from a cheap inverter (not possible with a conventional alternator):
Dirty output from a low quality conventional generator:
Clean output from a high-end inverter:
Clean output from a good conventional generator:
A good inverter generator and a good conventional generator can both provide good power. A modified sine wave inverter will likely do worse than even a cheap conventional generator, as long as the conventional generator is working properly. This is the reason why a modified sine wave inverter is very rarely used on generators (since they can just make a conventional generator in this case).