In every objective measure, vinyl is unquestionably inferior to CD. Significantly so.
Yet still, some people prefer vinyl. This is partly because they prefer the sound; but it is also about other factors as well. The "theatre of vinyl" - that is the setup of the deck, the cleaning of the stylus, the caring for the discs - is a big part of the attraction. Just like lacing up a 1/4" tape. This increased "interaction" makes you feel more connected to the music.
What about the sound itself? It needs to be separated out into two distinct areas: (1) what the medium (vinyl) does to the audio signal, and (2) how the signal is modified before it is fed into the cutting lathe.
Taking (1) first, it's clear that you have much less dynamic range on vinyl. You might get 60dB if you were lucky. Whereas 16 bit digital audio offers over 90dB. A clear and unambiguous victory. Whether anyone needs more than 60dB at home is questionable - what is the noise floor of a typical lounge? 30dBA? How loud do you play? 90dBA when head-banging...
In terms of frequency response, there are no limitations with CD. You can record any frequency in the audio band at any level you want, at any part of the stereo sound-stage. With vinyl, too much bass - especially panned away from the centre of the image - will render a record untraceable. Too much treble will overheat the cutting lathe.
With CD, harmonic distortion is a non-issue. With vinyl, the THD is about 1% at best - varying with frequency, and getting worse with every playing.
Not to mention speed variations, off-centre holes, warps, etc, etc.
Following on, (2) is about modifying the signal in the light of all these limitations. A "mastering engineer" will compress (reduce the dynamic range) of the signal - turning up the quiet parts of the performance so they don't become lost in the noise of even virgin vinyl. The bass end will be examined - often resulting in the peak levels being limited, but also applying compression to bring up the average level, so the loss of peak level isn't so noticeable. Of course, the bass content has to be mixed to mono. Similar comments apply to the HF end, as not only do you have to restrict the level for the sake of the cutting head, but you have to consider how things will sound once the record has had a few plays. It's a minefield.
Back in the day, good vinyl mastering engineers really earned their fees. They were an essential step between the recording studio and the cutting lathe, and they were very skilled at squeezing out the best results from a medium that is technically very poor indeed.
It's this "mastering" process that makes direct AB comparisons between vinyl and CD impossible. When you compare two nominally identical recordings, no matter how good condition the vinyl might be in, you can't eliminate the effect of the mastering process from the audio you hear.
In a way, it's this "mastering" process that gives vinyl a "rich" sound. We like compression, we like distortion. We like high frequencies to be gently curtailed. The mastering engineer will be trying to achieve a sound that sounds OK in a range of different situations - from a Dansette upwards - so will be doing everything he can to make a "nice" sound that is not too demanding from a technical point of view.
In a way, mastering isn't required for CD - the completed mix that comes from the recording studio would "fit" on the CD with no loss, and the joy of CD is that it potentially offers us the chance to hear what the mix engineer heard. But mastering is still done - mostly because few people listen on good hi-fi systems. Sometimes mastering is done in a very bad way (loudness wars), but whatever the merits, the mastering for CD will be different for vinyl and different for download. It will be different for SACD as well, so if you hear differences with SACD (compared to CD), that'll be what you hear - not the medium (24/192 is total overkill for delivery to the home, and adds nothing to the performance in a technical sense that we can actually perceive).
In a way, re-mastering is nothing more than a marketing opportunity. It is very rare to find a remastered CD that sounds better than the original. Most remasters are a crude application of compression and limiting to make it sound "bigger". The classic example being "Brothers In Arms", where the original has a staggering dynamic range (for a rock/pop recording). The PMR (peak to mean ratio) is 25-30dB or more in places. A typical modern rock/pop recording would be well under 10dB. The remastered version of Brothers In Arms is about 10-12dB, and sounds very dull as a result.
Ultimately, one might well have a strong preference for the vinyl - and expressing that preference
is fine because that's a subjective opinion based on all sorts of factors - not just the sound. But sadly, those that claim that vinyl is a better
medium than CD are making an objective statement that is demonstrably wrong. If you prefer vinyl, you prefer high amounts of harmonic distortion, a less dynamic sound, and less high and low frequency energy. And you enjoy all the paraphernalia that surrounds vinyl replay. Absolutely nothing wrong with that preference
CD as a medium is potentially "blameless". It's just a shame that the record companies choose to abuse it. There are some staggeringly good CDs out there, but they are hard to find.
Personally, I occasionally play vinyl, and it's good fun. It has no right to sound as good as it does - it's very enjoyable. But a CD that hasn't been messed about with at the mastering stage is simply light-years ahead.