Tube amplification sounds different from SS in many ways. The differences are subtle, but they add up: the listening experience with tubes is unlike solid state. Even compared to "somewhat warm" (read "tube-like") SS, tubes often have distinct qualities & strengths.
Based on hearing tube amps on speakers as well as headphones, IMO the biggest single difference is a 3-dimensional, palpable quality to musical notes with tubes. Pretty much any instrument or voice will sound "rounder," more real, more "there" on tubes. Closely related to this is a more expansive, tangible sense of the space in which music was performed & recorded. Not sure how or why, but I hear the acoustic space more clearly on tubes.
Years ago I was listening to a symphony orchestra (vinyl) on a big 100 WPC tube amp, and in a soft passage, the triangle was struck once. It was amazing how real & "there" that note was. When I closed my eyes, that percussionist & triangle were right there in my living room. That's a typical tube amplification experience...
Tubes aren't perfect world, of course. The trade-offs typically are some extension loss at the top & bottom frequencies. Many SS amps are more dynamic than tube amps, particularly at the frequency extremes. But these are generalities, not hard & fast rules. Some tube amps are blazingly fast, dynamic & wide-band; others are more intimate, diffuse & warm.
In my experience (significant but not definitive/vast), you're more likely to get a "liquid" sound signature w/tubes than SS, assuming the amps are well designed & executed. It may cost you an arm & a leg, though.