This is a commonly held misbelief - that metal dome tweeters sound harsh or bright, and that soft dome tweeters do not.
In most cases, the real culprit is the woofer. There is a natural bump in a woofer's response in the upper midrange (3-6 kHz), caused by a resonance coming from where the cone meets the flexible surround. Most woofers have at least a little of this, but some have quite a bit. In general, it seems that the stiffer the cone material is, the worse these resonant bumps are. Many metal woofers suffer from this problem, but others with various fiber reinforcement, like kevlar or fiberglass, also have it.
This upper midrange noise can result in an irritating edge to a speaker's sound. Speakers that at first seem to add detail over and above what is in the recording generally suffer from these kind of upper midrange peaks. Not surprisingly, many people mistakenly believe this fatiguing sound comes from the tweeter and not the woofer. This upper midrange emphasis is often combined with a dip in the crossover region (usually 2.5-3 kHz) due to sub-optimal crossover slopes. Some commercial designs seem to have deliberately done this to compensate for the woofer's high frequency resonance bump.
A properly designed crossover will take a woofer's upper midrange peaks into account and filter them enough so that sound is inaudible.