Has anyone been able to define well or measure differences between vinyl and digital?

First of all I would suggest a blind listening, switching from CD to Vinyl. Humans are full or bias, what you hear may be because it is what you want to hear.  For example when listeners listened to music with various speaker cables, they always said the music played thru thicker speaker cables sounded better than thru lamp cord.  However, that was only when they saw that it was thicker cable.  When lamp cord was disguised as a thick cable they thought the disguised lamp cord sounded better than the normal lamp cord.  Also blind tests showed that most people could not tell the difference between music played over You Tube compared to the same music played from a CD. To me I can always hear the difference between vinyl and digital because digital has none of the dust pops or crackle in quiet sections of the music.

On the bench CD and digital blows away vinyl.  Vinyl wins in the romantic, tactile, visual departments.

@prosdds , there is value in a blind test, but there is no point doing that test for vinyl and CD. The noise, even the faintest clicks/pops, will quickly identify the vinyl. Even if it did not, you would need 1 of each mastered exactly the same. Does that exist? Is there a test record that matches a test CD?  After that you need a perfectly set up turntable. Nice to test to aspire too, practically impossible.

@asctim , @grislybutter , I think they are on the right track. @asctim has provided concrete differences between CD and vinyl. @grislybutter talks about learned responses or learned likes. If you tie your self worth to your likes and purchases, then you may be inclined to argue that those likes and purchases are inherently better, not just for you, but for everyone. Maybe it is just the mastering, but I am inclined to believe it is the flaws in the vinyl that often give it that special magic. Not always, not even 50% of the time for me, but when it works, it works really well. For me, it does not need to be superior technically for me to like it.

For discussion accuracy, vinyl, tape, and analog are not the same thing. Vinyl and tape are storage mediums that are predominantly analog in nature. What would perfect analog sound like? Digital!! :-)

@mahler123

With all this esoterica being discussed, how does one account for the phenomena of the fact that most lps these days use digital files, and vinylista think they sound great, as long as they don’t know the truth?

Thinking in terms of LP vs Digital dichotomy doesn't explain it. More nuance is needed. At the very least, the Digital formats needs to be split onto Below The Transparency Threshold and Over the Transparency Threshold.

The Transparency Threshold depends on nature of music and hearing abilities of listener. It is different between typical pop music and untrained listeners vs classical symphonies and professional musicians or sound engineers.

Since this is an audiophile forum, I prefer to talk about the High Transparency Threshold. Here I deliberately use terminology different from official, e.g. High Definition Audio, to keep it free from marketing attachments.

In my previous posts, I gave hints as to why I believe CD format is significantly below the High Transparency Threshold, whereas 192/24 PCM and DSD128 are slightly above it. Going into even more detailed technical discussions here does not appear fruitful.

So, as I understand it, if an LP is pressed from a digital format that is over the High Transparency Threshold, it ought to sound no different compared to one pressed from an analog studio master of the same recording.

Finally, after all this science, we get to enjoy the music. Imagine that.