Digital LP’s

I think syr1990 has it right.  It all depends on the mastering.

I think one of the main reasons that some audiophiles prefer a vinyl version of a digital recording is that their cartridge has a non-flat frequency response that they like the sound of. Phono cartridges have been used for decades to tune the sound of a system. Some are bumped up in the mid bass, others have a hot high end response. That was always part of the fun of vinyl. CD players on the other hand have ruler flat frequency responses.

My experience is different than @rvpiano . I have many titles on CD and vinyl and I don't find that the vinyl version sounds inherently worse. In fact they often sound remarkably similar. When I got a Hana SL cartridge my vinyl rig began sounding much like the CD. If a CD lacks spaciousness and detail compared too the vinyl version I would suggest that the reason is that the cartridge has a tilted up response in the high frequencies which is responsible for the difference in sound.

I am unaware of any examples of a digitally recorded album being less compressed for the vinyl version than the CD version. If anyone has examples of this I would be interested in knowing what they are. 

There's still loads to unpick in this interesting discussion.

The vinyl production process is different to that for CD because on top of the choices made by the mastering engineer, the cutting engineer has to make a set of additional choices over and above those made by the mastering engineer as and between bandwidth, dynamic range and running time. So most of the time, the sound of what goes on to the final analogue reproduction medium can never be the same as what goes onto the digital.

By the way, I have very high resolution CD/SACD, Vinyl and Streaming front ends and I'm not biased towards any one of those. However, if I am going to purchase a digital recording, I'll do so on a digital medium rather than having that recording put through an additional step in being transcribed to vinyl.

I have a BMG record club LP of Pat Metheny's Still Life (Talking) from 1987 and the CD version.  The digital record, mastered by the great Bob Ludwig, has sounded better in some respects when I've compared it to the CD.  It's been a while since I did the comparison, but IIRC the bass ostinato on "Last Train Home" was more articulate on the LP than the CD, which surprised me.  I'll be getting a new cartridge soon, and I'm using a different DAC now, so I may repeat the comparison.

With analog-recorded albums, I have some where the CD sounds better and some where the LP sounds better.  It probably does come down to the mastering of each, as others above had said. I think Todd Rundgren's A Wizard, A True Star was one which sounded a little better on CD, not surprising given how each LP side is about 30' long.  Granted, that is a rather poor-sounding recording to begin with, but I love the music anyway.

Today's recordings are all high-res digital masters. Releasing them on vinyl format isn't meant to improve the sound quality at all. From the artist's and label's standpoint, vinyl releases (limited or standard) is to make a higher profit margin per unit sold. The sound quality of vinyl, even today's vinyl won't be as good as the high-rez digital recording because vinyl has medium format limitations. This is why recent vinyl remasters and even new releases will have a compressed dynamic range to fit the format or the producer's remastering goals.

CDs don't suffer from the same dynamic compression issues that vinyl does because the format can hold more information.  A caveat to this is when you have a double vinyl release that has 2 or 3 songs, max per side of vinyl. In this case, they're allowing the vinyl the opportunity to show its potential as a music format.

I also think one has to be aware when buying either vinyl or CDs, of the time period in which the original recording was released. Pre-CD ear, many albums sound better on vinyl, post CD-era when vinyl releases were going away, the original CD release will sound better than a post-CD era vinyl re-master. 

Then there are examples of my recent digital purchases of high-res recordings when I buy the CD. I've listened to both and they sound identical in soundstage, dynamic range and clarity.

My recent vinyl purchases tend towards completing an artist's catalog in my collection or original used 1st/2nd pressing vinyl. I don't prefer any particular format over the other because when I'm critically/purposefully listening to an album, I listen in the best format that I have.