Ribbon tweeters that I've heard do have a cleaner, less noisy sound to my ears. But like all broad generalizations, it depends on the ribbon tweeter and its implementation into an overall speaker design. Many ribbon drivers (but not all) used as tweeters in 2-ways, tend to have less ability to handle lower frequencies, below 3,000 Hz, limiting their use with many mid-woofers. In 3-way designs, they can be crossed at higher frequencies and avoid trouble. So how a ribbon sounds can depend on the crossover frequency.
Distortion
If I understand correctly what Zaph does with his harmonic distortion measurements, he stimulates drivers with lower frequency tones, and measures the various amounts of higher frequency harmonic distortion that results. This is done independent of any cabinet or crossover. Obviously, if a crossover filters out some or most of the primary tones that generate the worst of the harmonic distortion, the result will be quite different. Mounting a tweeter in a cabinet also has a large effect on the lower treble frequency response. So talking of a tweeter’s harmonic distortion generically, without considering cabinet or crossover may be painting with too broad a brush.
Vertical dispersion
In my opinion, too much is made of the issue of vertical dispersion. Taller ribbons with the ability to cover the upper midrange and higher do have limited vertical dispersion, but the small sized ribbon drivers that serve as tweeters are hardly effected by this.
Flat Impedance Curve
Most ribbon tweeters that I seen have little or no rise in impedance as frequency increases. This essentially flat impedance vs. frequency curve makes crossover design much easier than with a dome driver with a typical voice coil.