The TL431 is probably less noisy.
(Bandgap references, like TL431, are notoriously noisy, as solid state signals go; but glow discharges are so awful, they've been used as
noise sources (with some tweaks, namely, magnetic bias).)
Also, you seem to be under some illusion as to the value of VR tube stability -- few tube circuits needed it, indeed few circuits
in general need regulation. It's just done as a matter of course because, if we're starting with a 90-250VAC line spec, we can't very well work directly with that, and the output is usually variable anyway (e.g. flyback power supply) so the output must be stabilized with feedback regardless, and we might as well use a puny cheap TL431 or the like, as an error amplifier, to provide that feedback. The fact that a TL431 happens to give a <= 5% precision (and typically ~0.1% stability) is practically accidental, but we aren't going to argue with results that are both good and cheap.
The average tube circuit consists of a few amplifier stages, which will amplify equally well over perhaps a +/- 20% range of supply, give or take reduced gain or maximum power output at the low end, and reduced lifetime at the high end (excessive plate or heater dissipation; cathode wear). Unless you have 3rd-world mains (in which case the bigger problem is usually just that it's terribly unreliable..?), an unregulated, mains-derived supply will do fine.
Tim
P.S. A motor vehicle gets "chocked" to prevent it from rolling away. Short, harder 'ch'. You might be
shocked (soft 'sh') to discover something though. English, right?...