All I can do is to offer an untested theory. Both circuits are phase-shift oscillators and thus they should produce sine wave outputs. So, why should sine wave "A" as a modulating signal sound different than sine wave "B"? It shouldn't.
However...(I have not tested this ) I don't know whether whether ALL phase shift oscillators output pure sine waves. For the most part, when you look at PS osc schematics in the idealized form, one generally sees a: triodes, and b: three identical R-C networks, the caps and the R's all equal. I can readily believe that would output a clean, symmetrical sine wave.
What I *can* tell you from direct experience is that a low-frequency phase-shift oscillator that isn't running a high-gain (12AX7) tube but instead is running on a low-gain 12AU7 can take a remarkable amount of time to build up to its ultimate state of self-sustaining oscillation. I know this because I have breadboarded such a circuit. I am not talking about how much time it takes for a dead-cold tube to light up and start working, I'm talking about a tube shut off in such a circuit, then B+ applied again.....with the filament still hot, though not lit up. It can take 3-4 seconds for such a ckt to start up upon application of fresh B+ with an already-hot filament.
With possibly-leaky old caps (like I used because I was just goofing around with junkbox parts) and a weak old 12AU7, it might not start at all! Same circuit with a good 12AX7 will start right up. It's quite noticeable, not subtle at all.
Bottom line: With a much higher gain pentode in place of a triode, it would not surprise me to find a different output waveform with a more aggressive slope, and certainly a more rapid and reliable startup of the oscillator.
I think, if my curiosity was tweaked as you are suggesting yours is, I would breadboard just the trem oscillator in a way that I could scope it (not that easy to see very low freqs on a scope) and lash it into an existing amp to see how I liked it.
Me? I never use tremolo, LOL.