pull out some tube rect data sheets and compare them with SS diode data sheets, then think about what causes sag in an unregulated circuit, and where. While you're doing that think about the size of filter caps seen in the circuits in question.
for the truly curious, buy and restore one of those Heathkit or Eico variable bench supplies, and experiment with powering your other tube gear with it, instead of using whatever you're using currently.
The difference can be similar to listening to different DA converters, or changing your recording resolution, or other similar potentially hairsplitting change. I have regulated tube supplies, unregulated tube supplies, and the normal SS supplies. You won't get a definitive answer out of me. I use what's practical and convenient for the job. Sometimes hairsplitting makes the difference. The most positive experiences I 'think' I've noticed with some tube rectifier supplies in some situations was a cleaner/clearer mid and treble, and a slightly less flat sound. Is that enough disclaimers and prerequisites for one sentence? I think I've seen something about tube rectifiers putting out far less high frequency trash than some diodes, and if that's at all true could account for what I've heard a few times.
I'm not losing sleep. Not rushing to replace diodes with tubes. Not rushing to replace tube rectifiers with diodes. If I'm building a tube piece, and I have the right power trans for tube rectification, I'll probably use it and go that way. I doubt I'd ever hand-roll a regulated tube supply. But if I have one sitting around I'll likely use it first, assuming it's right for the job.