As for tube amps, at least there's one area where there's no question about the difference: Guitar amplifiers. There the amp itself is part of the sound, you're not after pure amplification at all, you want to hear what the amp adds by overdriving it. Overdriving a solid state amp sounds totally different. So vacuum tubes never went away, there was never a period where solid state "took over" for tubes, when it comes to guitar amplifiers.
Specifically, when you "overdrive" a tube amp, you drive the output stage into incipient clipping, which adds some even-order harmonic distortion to the sound. Doing the same thing with a solid state amp results in "hard" clipping, which generates disagreeable odd-order harmonic distortion. With solid state amplification, as soon as you go off the linear part of the gain curve the distortion hits, and hits hard. Tube circuits make the transition much more gradually, which not only produces a more pleasant effect, it gives the musician greater control.
(Acoustic guitar amplifiers though - there you don't want to hear the amplifier colouring the sound at all, so solid state is (generally) the rule there.)
No reason for that. In general, tube amps are as linear as their solid state counterparts and often have better transient response, producing a more natural sound. As long as the amp is operated in the linear part of its gain curve it won't color the sound.