I have heard that brushless generators have really dirty power. At least one oscilloscope trace seemed to verify that. The sine wave looked halfway to a squiggly sawtooth. That makes no sense to me, but maybe I don't understand how rotating field generators work.
Based on my experience, I would not make that particular assertion. Clean, or dirty power arises from lots of sources; choices in winding design, choices in voltage regulation, choices in rotor design/construction, and of course maintenance and tuning.
To the extent that brushes aren't in good shape and in the commutator design is not good, you can get a lot of noise out of a brushed design.
I think a lot of this comes down to the quality of the pieces of the generator and the overall construction.
I have a couple of inexpensive generators that I use to power things like 120V tools in remote locations. Since they are just running a motor, often a cheap motor, I don't sweat the power quality ever. However, I have looked and the power was actually very good, but all it takes is a diode or a capacitor or a regulator to start dying and power quality goes out the window.
Running pricey home devices that are electronic? I think that is a different story; test and measure, and keep testing and measuring. As someone famous once said "trust, but verify", and for electronics, I would also add "use as many surge and EMI protectors as you can", as every little bit helps.
All the best,
Peter