I have had both a headphone system and main speaker system for the last fifty years. I have constantly upgraded both systems as I gained experience and wealth. I have spent an enormous amount of time listening to headphone systems, first as an exploration geologist that spent about 8 - 10 hours a day driving in the middle of no where and then as an executive that would travel a lot. When home I would listen to my main system.
Most of my experience was with all kinds of amps, but for a year or more each.
The most important trend of my systems was the move to tubes over time. All of my components are now tubed. That to me says everything. Never has my systems sounded nearly as good.
While it is definitely true that SS and tube gear have approached each other. Good quality tube gear sounds more like music… gets out of the way; has better rhythm and pace and emotional connection.
This is apparent, I’d have to say equally apparent in headphone or speakers systems… but highly dependent on the particular system. I have carefully chosen systems designed to be detailed a musical… and in mine, the magic of the tubes is easy to discern, although they in no way sound tubey.