My benchmark for this is to listen to the opening bars of Mahler's 1st, on CD you get a lovely quiet background with the music gradually emerging at least with a decent mastering, with vinyl, even well-cared for vinyl on a good TT you get a low level but quite audible set of noises added to it, this was true in 1984 when I went from a Rega to a 14 bit (x4) Marantz and is just as true now, listening on headphones the noise is more pronounced
The CD is limited by Information Theory constraints, vinyl is limited by the laws of physics.
Sadly neither often deliver all they are actually capable of, for different reasons.
[1] In the 80s Ivor (I'll never make a CD player) Tiefenbrun of Linn was unable to detect the presence of a Sony PCM-F1 a nominally 16 bit converter placed after the analog out from a Linn system and others (MatrixHifi - spanish vinyl lovers) have repeated the same test blind with better gear, so the digitization process itself does not appear to be overly audibly degrading.
That said there is something about vinyl that is very seductive and I see a gap between my Delta 70s big enough for a Turntable stand and my Rotel amp has a phono stage, part of me still wants to fill that gap though I know it is irrational, expensive and full of fiddle (record cleaners, new sleeves, static treatements...) but I grew up with vinyl in the 60s/70s/80s and some things are hard to shake off, I still have a box of Lps in an attic in Nuneaton.
But superior ? rationally LP is only *potentially* superior on a few parameters but see [1]