I think the question was referring to OTL tube vs SS amps, and one reason is the amplifier damping factor (DF), or the ability of the amp to control the headphone driver, or how quick the amp can stop the driver from signal to no-signal. The damping factor can be calculated as the headphone impedance divided the amp output impedance.
A high value may result in edgy treble and tight/punchy bass and a low value may result in smoother edges and more "boomy" bass. There is a DF range which make the listening experience "more pleasant" (too much or too few may result unpleasant), but this range depend on the driver technology and your listening preferences.
So for high impedance headphones, like the ones you mention, the DF is too high when using SS amps given its relative low output impedance. For example ZMF Verite headphones have beryllium drivers which deliver very quick transients (too quick??). The last specially take advantage of OTL amps (higher output impedance --> lower DF) slowing down the quick transient of the VC, making the notes to have more presence, fading away slower which result in a more relaxed listening experience.
On the other hand, planar magnetic headphones (lower impedance) seems to be preferred with SS amps (better DF), given that now the DF maybe "too low" when paired with tube amps.
You see also recently the trend of amp manufactures to provide different setting for the output impedance, so they can have better match with different driver technologies.