Great questions. I don't know if there can be a definitive answer. These are all just tools that different artists will respond to differently. Few thoughts:
I think in general analog sounds interesting because of imperfection, distortion, non-linearity, saturation, temperature dependency (being slightly off, slight out of tune etc.), also being able to avoid aliasing. Another aspect of it is being able to have continuous voltage control of parameters rather than mapping something to 0-127, etc. I personally feel like I can hear an obvious difference, but it's hard to say if that holds in general. I'm also the kind of person who hears tube guitar amps as obviously better than solid state or modeling. It really depends on what you're doing. It would be interesting to try to A-B test similar filter implementations in both domains, like say a Moog Ladder. To my ears, the difference is obvious.
Some operations just have fundamentally different behavior/meaning in the analog domain: I'm thinking of gain and summing in particular. You're able to avoid losing dynamic range. Also clipping vs saturation: for example, you might intentionally saturate in analog, but you're probably going to try to avoid clipping in digital at all costs.
My sense is that the fundamental differences between analog and digital dominate over component variation effects when it comes to sound. An FPAA implementation is essentially an opamp implementation. An opamp implementation of a filter design is closer to an implementation made out of discrete transistors than it is to a purely digital implementation. At this point we start getting into the weird territory of worrying about "the sound" of an integrated circuit vs a discrete transistor or exactly what transistor material is being used. I think it's clear that analog integrated circuits can sound great; there are a bunch of classic ones. They're very similar in terms of material but different architecturally. I don't think someone would confuse one of these ICs with similar digital algorithms just because they're built out of integrated silicon rather than discrete transistors.