My answer is: tubes, every time.
But the logic of this question presumes that tubes act as some kind of tone control–ie, that they alter/adjust/enhance tonality.
I have long experience w/big tube amps in 2-channel systems, and have had a couple tube amps in headphone audio. IMO what tubes do the sound is way more complicated (and potentially beneficial) than any tonal changes:
1 - I’ve always found the biggest different in tube sound to be the enhanced dimensionality of notes, a greater sense of realness. Notes sound like things occurring in space, with a beginning & a decay. Notes become more palpable, less like blips on a FC curve.
2 - Tubes also depict space itself (the recording venue, subtle acoustic cues as to position of instruments, singers, walls, floor, ceilings, audience if any) with far greater naturalism & fidelity than SS. There are always exceptions, but generally, tubes will smoke SS in this regard
3 - Yes, there are tonal changes with tubes, but they’re often rather subtle, perhaps not at all what you might expect if you think of tubes as EQ filters. I’ve certainly heard tubes that sounded warm up top, mid-bassy but lower in dynamics/impact in the bass, with big/huge mids, etc (classic tube sound). But tubes can also be used in an amp “voiced” to be neutral; in these cases, the designer declines to use tubes as EQ filter–but makes full use of their 3D palpability & ambient realism.
Example: I have the humble but very nice OTL, the Woo WA3. I’ve heard many headphones on it (it works very well with high impedance HPs, as you’d expect–but also very well with planars). I can’t ever remember hearing a headphone on the WA3 and finding the sound to be warm, syrupy, slow, bass-shy, any of those things. Instead, what I typically hear is a rather calm, controlled, neutral/unhyped sound that seems very dimensional & real.