I listen to vinyl myself, and I also have some limited knowledge of the science involved. I don't claim to be any sort of an expert in acoustics but I do have a basic grounding in DSP from my undergraduate days as well as high-school physics to refer to ...
I have to say I enjoy vinyl for a number of non-qualitative reasons. Nostalgia. Tactility. The cover art. The fact that the medium feels like it has more of a "wholeness" to it. My system is fairly modest: A pair of battered Technics turntables plugged through a mixer as preamp into a bog-standard stereo. It's certainly not audiophile quality.
But I am constantly struck by how visitors comment on the sound quality when I play my records for them. To a certain extent, I can put it down to a placebo effect, but many often refer to a "warmer" sound. Even with the dust-crackles and occasional pops!
There are a couple of things I could think of that could explain it. Firstly is that the accepted human range of hearing is 20 Hz to 20 kHz .. from what I recall of CD sampling it is set at 44.1k samples per-second, twice the dynamic-range in anticipation of Nyquist aliasing.
I can't help but wonder if there are "inaudible" frequencies that are chopped out in this scheme. The deep bass-tones that our ears don't pick up but are felt in our body. These frequencies could resonate external physical fixtures perhaps creating a more immersive acoustic experience.
I've also heard it been said that these inaudible frequencies can be picked up by the body, in particular the stomach and chest cavity, which could give the sound a more visceral quality. Certainly this is the case in a club or even a lounge setting. Apart from being able to physically scratch and manipulate this would also explain why vinyl has persisted moreso in these environments.
Aside from this acoustic hocus pocus there might be a more fundamental reason for perceived qualitative differences, and that is to do with implementation. CD as a technology is sufficiently provisioned to capture the entire range of human audio, but for reproduction you are always at the mercy of your DAC.
It's important to remember that when you're listening to digital sound you are listening to an analogue signal that's reproduced by modulating an oscillator, whereas with an analogue recording you're listening to the original analogue signal.
This isn't an issue for well built sound system but is that most people's experience? Whereas whenever we listen to records the DAC simply isn't an issue. This may not result in "better" sound but it would make it distinguishably "different". I remember being struck, when repairing one of my turntables just how little electronics there was on the audio line: Pretty much a straight uninterrupted line from the stylus out to the pre-amp.
One final thought is that, who even listens to CDs any more? We're so used to listening to music on our phones or computers, from a number of formats at varying compression levels and of varying quality, through poor quality headphones or car stereo systems. It could just be that our expectations have been slowly been lowered by ever decreasing reductions in quality to the point that when we do hear something reproduced as its master intended it is a notable experience.