Without trying to provoke an Audiophoolery war
...
The one difference I can see between oil caps and other types is ... well, the oil. I've used oil caps (the Russian mil ones) in speaker crossovers very successfully - they do sound cleaner there. I think the reason is simple mechanical damping of the plates provided by the oil, maybe that and the fact that they are foil and not metalized. We all know that film caps can sing (ceramic too), I've never heard an oil cap even whisper.
Of course that's in crossovers where there's significant ac current and voltage swing across the caps. In low level coupling (or maybe filtering) applications, that's a different matter, maybe (probably )dielectric properties are the dominant factor, maybe at low levels sensitivity to mechanical vibration damping matches the miniscule stresses generated. Who knows. I'm not going to stick my neck out on that one.