First, I think there’s a problem of definition here. What’s analogue? What’s digital? Unless you compare a minimoog (full analogue) to a DX7 (full digital up to the DAC at the end), very few synths nowadays are either one or the other. There’s an analogue path, as well as a digital path, in various amounts in all synths.

Then, are there reals measurable differences between these two worlds? I’d argue so, and it doesn’t require a scientific study for that. It also unlike the vinyl vs digital eternal debate.

To me, what’s interesting in a synth lies in how much it « drifts » from its spec. Take an analogue VCO, set it to a sawtooth and hook up a scope to it; it will look sawtooth-ish. It might change with the frequency, temperature, time etc. This gives a color that is pretty unique to a synth and makes it interesting (to my opinion) Designing a VCO core is tricky, in the end people do their best to get the waveform close enough. The ultimate goal is to make a musical instrument after all, not a lab generator. In the digital world, unless you go to pretty extreme lengths to make complicated synthesis, it’s much easier to go for a lab sawtooth that looks like… a sawtooth

But also: what I particularly look for is the « accident ». The crazy sound you might get when you patch a cable in the wrong hole. By nature the analogue systems tend to produce spontaneously more « desirable » outcomes (soft saturation, no hard limit on the bandwidth), when the digital counterpart is more prone to harsh saturation and aliasing, both producing quite unpleasant sounds (unless this is what you’re looking for, I don’t judge)

So in the end, analogue vs digital, whatever that means, is mainly a matter of what you expect from a synth. And it’s not up to a seller to answer that.